Timeline for Sum of 'the first k' binomial coefficients for fixed $N$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 5, 2017 at 23:34 | comment | added | Brian Hopkins | The $k=5$ case, 1, 2, 4, 8, 16, 31, 57, ... (oeis.org/A000127), is a common "counterexample" in discrete mathematics courses that nice patterns (here, powers of 2) do not always hold. A direct formula is $(n^4 - 6n^3 + 23n^2 - 18n + 24)/24$. An interpretation is the greatest possible number of regions given by drawing secants between $n$ points on a circle. See Honsberger, Martin Gardner, Conway & Guy's Book of Numbers, etc. | |
| Dec 3, 2015 at 14:53 | review | Suggested edits | |||
| Dec 3, 2015 at 15:29 | |||||
| S Sep 17, 2015 at 23:20 | history | suggested | Thomas Dybdahl Ahle | CC BY-SA 3.0 |
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| Sep 17, 2015 at 23:03 | review | Suggested edits | |||
| S Sep 17, 2015 at 23:20 | |||||
| Mar 6, 2010 at 3:32 | comment | added | Douglas S. Stones | There's a generating function there too: (1 - xy)/((1 - y - xy)*(1 - 2*x*y)). Also, for k=2,3,...,10 it's given by Sloane's A000124, A000125, A000127, A006261, A008859, A008860, A008861, A008862, A008863. | |
| Mar 6, 2010 at 3:24 | history | answered | Douglas Zare | CC BY-SA 2.5 |