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 A055795 a(n) = binomial(n,4) + binomial(n,2). 16

%I

%S 0,1,3,7,15,30,56,98,162,255,385,561,793,1092,1470,1940,2516,3213,

%T 4047,5035,6195,7546,9108,10902,12950,15275,17901,20853,24157,27840,

%U 31930,36456,41448,46937,52955,59535,66711,74518,82992,92170,102090,112791,124313,136697

%N a(n) = binomial(n,4) + binomial(n,2).

%C 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?

%C 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

%C Antidiagonal sums of A139600. - _Johannes W. Meijer_, Apr 29 2011

%C Also the number of maximal cliques in the n-tetrahedral graph for n > 5. - _Eric W. Weisstein_, Jun 12 2017

%H James Spahlinger, <a href="/A055795/b055795.txt">Table of n, a(n) for n = 1..1000</a>

%H Michael Boardman, <a href="http://www.jstor.org/stable/3219201">The Egg-Drop Numbers</a>, Mathematics Magazine, 77 (2004), 368-372.

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>

%H Alexsandar Petojevic, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL5/Petojevic/petojevic5.html">The Function vM_m(s; a; z) and Some Well-Known Sequences</a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JohnsonGraph.html">Johnson Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalClique.html">Maximal Clique</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TetrahedralGraph.html">Tetrahedral Graph</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

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

%F a(1) = 1; a(n) = a(n-1) + 1 + A004006(n-1).

%F a(n+1) = C(n, 1) + C(n, 2) + C(n, 3) + C(n, 4). - _James A. Sellers_, Mar 16 2002

%F Row sums of triangle A134394. Also, binomial transform of [1, 2, 2, 2, 1, 0, 0, 0,...]. - _Gary W. Adamson_, Oct 23 2007

%F 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

%F a(n) = n*(n^3-6*n^2+23*n-18)/24. - _Gary Detlefs_, Dec 08 2011

%F 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

%p A055795:=n->binomial(n,4)+binomial(n,2); # _Zerinvary Lajos_, Jul 24 2006

%t Table[Binomial[n, 4] + Binomial[n, 2], {n, 50}] (* _Vladimir Joseph Stephan Orlovsky_, May 24 2009 *)

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

%t LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 3, 7, 15}, 50] (* _Harvey P. Dale_, Dec 07 2015 *)

%t Total[Binomial[Range[20], #] & /@ {2, 4}] (* _Eric W. Weisstein_, Dec 01 2017 *)

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

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

%o (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 */

%o (PARI) a(n)= n*(n^3-6*n^2+23*n-18)/24 \\ _Wesley Ivan Hurt_, Sep 29 2013

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

%Y Cf. A134394, A051601.

%K nonn,easy

%O 1,3

%A _Clark Kimberling_, May 28 2000

%E Better description from _Leonid Broukhis_, Oct 24 2000

%E Edited by _Zerinvary Lajos_, Jul 24 2006

%E Offset corrected and Sellers formula adjusted by _Gary Detlefs_, Nov 28 2011

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Last modified December 14 12:28 EST 2018. Contains 318097 sequences. (Running on oeis4.)