Could someone explain the proof of Cake Numbers?












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Is there a graphical, or visual, proof of the Cake Numbers? And if so, could someone explain it to me? I am looking for an explanation similar to that for the Lazy Caterer's sequence on Wikipedia: https://en.wikipedia.org/wiki/Lazy_caterer%27s_sequence
Thanks










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  • $begingroup$
    The Cake Numbers $1,2,4,8,15,26,...$ describe how many pieces can be formed by making $nge 0$ straight cuts into a cake or a ball. The formula is $binom{n}{0}+binom{n}{1}+binom{n}{2}+binom{n}{3}$, with terms being zero of course when the second argument exceeds the first.
    $endgroup$
    – Oscar Lanzi
    Jan 12 at 14:34


















0












$begingroup$


Is there a graphical, or visual, proof of the Cake Numbers? And if so, could someone explain it to me? I am looking for an explanation similar to that for the Lazy Caterer's sequence on Wikipedia: https://en.wikipedia.org/wiki/Lazy_caterer%27s_sequence
Thanks










share|cite|improve this question









$endgroup$












  • $begingroup$
    The Cake Numbers $1,2,4,8,15,26,...$ describe how many pieces can be formed by making $nge 0$ straight cuts into a cake or a ball. The formula is $binom{n}{0}+binom{n}{1}+binom{n}{2}+binom{n}{3}$, with terms being zero of course when the second argument exceeds the first.
    $endgroup$
    – Oscar Lanzi
    Jan 12 at 14:34
















0












0








0





$begingroup$


Is there a graphical, or visual, proof of the Cake Numbers? And if so, could someone explain it to me? I am looking for an explanation similar to that for the Lazy Caterer's sequence on Wikipedia: https://en.wikipedia.org/wiki/Lazy_caterer%27s_sequence
Thanks










share|cite|improve this question









$endgroup$




Is there a graphical, or visual, proof of the Cake Numbers? And if so, could someone explain it to me? I am looking for an explanation similar to that for the Lazy Caterer's sequence on Wikipedia: https://en.wikipedia.org/wiki/Lazy_caterer%27s_sequence
Thanks







sequences-and-series proof-explanation






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asked Jan 12 at 11:52









BanchettiBanchetti

1




1












  • $begingroup$
    The Cake Numbers $1,2,4,8,15,26,...$ describe how many pieces can be formed by making $nge 0$ straight cuts into a cake or a ball. The formula is $binom{n}{0}+binom{n}{1}+binom{n}{2}+binom{n}{3}$, with terms being zero of course when the second argument exceeds the first.
    $endgroup$
    – Oscar Lanzi
    Jan 12 at 14:34




















  • $begingroup$
    The Cake Numbers $1,2,4,8,15,26,...$ describe how many pieces can be formed by making $nge 0$ straight cuts into a cake or a ball. The formula is $binom{n}{0}+binom{n}{1}+binom{n}{2}+binom{n}{3}$, with terms being zero of course when the second argument exceeds the first.
    $endgroup$
    – Oscar Lanzi
    Jan 12 at 14:34


















$begingroup$
The Cake Numbers $1,2,4,8,15,26,...$ describe how many pieces can be formed by making $nge 0$ straight cuts into a cake or a ball. The formula is $binom{n}{0}+binom{n}{1}+binom{n}{2}+binom{n}{3}$, with terms being zero of course when the second argument exceeds the first.
$endgroup$
– Oscar Lanzi
Jan 12 at 14:34






$begingroup$
The Cake Numbers $1,2,4,8,15,26,...$ describe how many pieces can be formed by making $nge 0$ straight cuts into a cake or a ball. The formula is $binom{n}{0}+binom{n}{1}+binom{n}{2}+binom{n}{3}$, with terms being zero of course when the second argument exceeds the first.
$endgroup$
– Oscar Lanzi
Jan 12 at 14:34












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