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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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