A055795 a(n) = binomial(n,4) + binomial(n,2).

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

Offset: 1

Author

Clark Kimberling, May 28 2000

Keywords

• nonn
• easy

Comments

Answer to the question: if you have a tall building and 4 plates and you need to find the highest story from which a plate thrown 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 do not have 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

Mark each point on an 8^(n-2) grid with the number of points that are visible from the point; for n > 3, a(n) is the number of distinct values in the grid. - Torlach Rush, Mar 25 2021

Antidiagonal sums of both A057145 and also A134394 yield this sequence without the initial term 0. - Michael Somos, Nov 23 2021

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).

Crossrefs

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

Cf. A134394, A051601, A057145.

Programs

Magma

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

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~ *)

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

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

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