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A063258 a(n) = binomial(n+5,4) - 1. 11
4, 14, 34, 69, 125, 209, 329, 494, 714, 1000, 1364, 1819, 2379, 3059, 3875, 4844, 5984, 7314, 8854, 10625, 12649, 14949, 17549, 20474, 23750, 27404, 31464, 35959, 40919, 46375, 52359, 58904, 66044, 73814, 82250, 91389, 101269, 111929, 123409, 135750 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

In the Frey-Sellers reference this sequence is called {(n+2) over 4}_{3}, n >= 0.

If X is an n-set and Y a fixed (n-4)-subset of X then a(n-5) is equal to the number of 4-subsets of X intersecting Y. - Milan Janjic, Aug 15 2007

For n>=5, a(n-5) is the number of permutations of 1,2...,n with the distribution of up (1) - down (0) elements 0...01000 (the first n-5 zeros), or, the same, a(n-5) is up-down coefficient {n,8} (see comment in A060351). - Vladimir Shevelev, Feb 18 2014

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

Guillaume Aupy, Julien Herrmann. Periodicity in optimal hierarchical checkpointing schemes for adjoint computations. Optimization Methods and Software, Volume 32, 2017 - Issue 3. Preprint

D. D. Frey and J. A. Sellers, Generalizing Bailey's generalization of the Catalan numbers, The Fibonacci Quarterly, 39 (2001) 142-148.

Milan Janjic, Two Enumerative Functions

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

FORMULA

a(n) = A062750(n+2, 4) = (n+6)*(n+1)*(n^2 + 7*n + 16)/4!.

G.f.: (x-2)*(x^2-2*x+2)/(x-1)^5 = N(4;1, x)/(1-x)^5 with N(4;1, x)= 4 - 6*x + 4*x^2 - x^3, polynomial of second row of A062751.

MAPLE

[seq(binomial(n+5, 4)-1, n=0..37)]; # Zerinvary Lajos, Nov 25 2006

MATHEMATICA

s1=s2=s3=s4=0; lst={}; Do[a=n+(n+2); s1+=a; s2+=s1; s3+=s2; s4+=s3; If[(s3-2)/2>0, AppendTo[lst, (s3-2)/2]], {n, -1, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 04 2009 *)

PROG

(PARI) { for (n=0, 1000, write("b063258.txt", n, " ", binomial(n + 5, 4) - 1) ) } \\ Harry J. Smith, Aug 19 2009

CROSSREFS

Fifth column (r=4) of FS(4) staircase array A062750.

A column of triangle A014473.

Cf. A000096, A062748.

Sequence in context: A011554 A099586 A253001 * A178964 A197275 A011852

Adjacent sequences:  A063255 A063256 A063257 * A063259 A063260 A063261

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jul 12 2001

EXTENSIONS

Simpler definition from Vladeta Jovovic, Jul 21 2003

STATUS

approved

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Last modified February 19 16:02 EST 2019. Contains 320311 sequences. (Running on oeis4.)