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A055795
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Binomial(n,4) + binomial(n,2).
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10
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0, 1, 3, 7, 15, 30, 56, 98, 162, 255, 385, 561, 793, 1092, 1470, 1940, 2516, 3213, 4047, 5035, 6195, 7546, 9108, 10902, 12950, 15275, 17901, 20853, 24157, 27840, 31930, 36456, 41448, 46937, 52955, 59535, 66711, 74518, 82992, 92170, 102090, 112791, 124313, 136697
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Answer to the question: if you have a tall building and 4 plates and you need to find the highest story, a plate thrown from which does not break, what is the number of stories you can handle given n tries?
If Y is a 2-subset of an n-set X then, for n>=4, a(n-3) is the number of 4-subsets of X which have no exactly one element in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 28 2007
Antidiagonal sums of A139600. [From Johannes W. Meijer, Apr 29 2011]
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REFERENCES
| Michael Boardman, "The Egg-Drop Numbers", Mathematics Magazine, 77 (2004), 368-372. [From Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Sep 30 2009]
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LINKS
| Milan Janjic, Two Enumerative Functions
Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
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FORMULA
| Differences give A000127. Also a(1) = 1; a(n) = a(n-1) + 1 + A004006(n-1).
a(n+1) = C(n, 1) + C(n, 2) + C(n, 3) + C(n, 4) - James Sellers, Mar 16 2002
Row sums of triangle A134394. Also, binomial transform of [1, 2, 2, 2, 1, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 23 2007
O.g.f.: -x^2(1-2x+2x^2)/(x-1)^5. a(n)=A000332(n)+A000217(n-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 13 2008
a(n)= n*(n^3-6*n^2+23*n-18)/24. [From Gary Detlefs, Dec 08 2011]
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MAPLE
| [seq(binomial(n, 4)+binomial(n, 2), n=1..50)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 24 2006
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MATHEMATICA
| Table[Binomial[n, 4] + Binomial[n, 2], {n, 50}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), May 24 2009]
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CROSSREFS
| T(2n+1, n), array T as in A055794. Cf. A004006, A000127.
Cf. A134394.
Sequence in context: A147400 A002545 A153114 * A058695 A187100 A182726
Adjacent sequences: A055792 A055793 A055794 * A055796 A055797 A055798
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KEYWORD
| nonn,easy
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), May 28 2000
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EXTENSIONS
| Better description from Leonid A. Broukhis (leob(AT)mailcom.com), Oct 24 2000
Edited by Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 24 2006
Offset corrected and Sellers formula adjusted by Gary Detlefs, Nov 28 2011
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