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A055795 a(n) = binomial(n,4) + binomial(n,2). 15
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; text; internal format)
OFFSET

1,3

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 Janjic, Dec 28 2007

Antidiagonal sums of A139600. - Johannes W. Meijer, Apr 29 2011

Also the number of maximal cliques in the n-tetrahedral graph for n > 5. - Eric W. Weisstein, Jun 12 2017

LINKS

James Spahlinger, Table of n, a(n) for n = 1..1000

Michael Boardman, The Egg-Drop Numbers, Mathematics Magazine, 77 (2004), 368-372.

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

Eric Weisstein's World of Mathematics, Johnson Graph

Eric Weisstein's World of Mathematics, Maximal Clique

Eric Weisstein's World of Mathematics, Tetrahedral Graph

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = A000127(n)-1. Differences give A000127.

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 A. Sellers, Mar 16 2002

Row sums of triangle A134394. Also, binomial transform of [1, 2, 2, 2, 1, 0, 0, 0,...]. - Gary W. Adamson, 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, Apr 13 2008

a(n) = n*(n^3-6*n^2+23*n-18)/24. - Gary Detlefs, Dec 08 2011

a(1)=0, a(2)=1, a(3)=3, a(4)=7, a(5)=15, a(n) = 5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - Harvey P. Dale, Dec 07 2015

MAPLE

A055795:=n->binomial(n, 4)+binomial(n, 2); # Zerinvary Lajos, Jul 24 2006

MATHEMATICA

Table[Binomial[n, 4] + Binomial[n, 2], {n, 50}] (* Vladimir Joseph Stephan Orlovsky, May 24 2009 *)

Table[n (n^3 - 6 n^2 + 23 n - 18)/24, {n, 100}] (* Wesley Ivan Hurt, Sep 29 2013 *)

LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 3, 7, 15}, 50] (* Harvey P. Dale, Dec 07 2015 *)

Total[Binomial[Range[20], #] & /@ {2, 4}] (* Eric W. Weisstein, Dec 01 2017 *)

CoefficientList[Series[x (-1 + 2 x - 2 x^2)/(-1 + x)^5, {x, 0, 20}], x] (* Eric W. Weisstein, Dec 01 2017~ *)

PROG

(MAGMA) [n*(n^3-6*n^2+23*n-18)/24: n in [1..100]]; // Wesley Ivan Hurt, Sep 29 2013

(Maxima) A055795(n):=n*(n^3-6*n^2+23*n-18)/24$ makelist(A055795(n), n, 1, 100); /* Wesley Ivan Hurt, Sep 29 2013 */

(PARI) a(n)= n*(n^3-6*n^2+23*n-18)/24 \\ Wesley Ivan Hurt, Sep 29 2013

CROSSREFS

T(2n+1, n), array T as in A055794. Cf. A004006, A000127.

Cf. A134394, A051601.

Sequence in context: A002545 A153114 A290865 * A058695 A228447 A187100

Adjacent sequences:  A055792 A055793 A055794 * A055796 A055797 A055798

KEYWORD

nonn,easy,changed

AUTHOR

Clark Kimberling, May 28 2000

EXTENSIONS

Better description from Leonid Broukhis, Oct 24 2000

Edited by Zerinvary Lajos, Jul 24 2006

Offset corrected and Sellers formula adjusted by Gary Detlefs, Nov 28 2011

STATUS

approved

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Last modified December 11 21:15 EST 2017. Contains 295919 sequences.