A095661 Fifth column (m=4) of (1,3)-Pascal triangle A095660.

3, 13, 35, 75, 140, 238, 378, 570, 825, 1155, 1573, 2093, 2730, 3500, 4420, 5508, 6783, 8265, 9975, 11935, 14168, 16698, 19550, 22750, 26325, 30303, 34713, 39585, 44950, 50840, 57288, 64328, 71995, 80325, 89355, 99123, 109668, 121030, 133250, 146370

Offset

0,1

Comments

If Y is a 3-subset of an n-set X then, for n >= 6, a(n-6) is the number of 4-subsets of X having at most one element in common with Y. - Milan Janjic, Nov 23 2007

Row 3 of the convolution array A213550. - Clark Kimberling, Jun 20 2012

Links

Table of n, a(n) for n=0..39.

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

Formula

G.f.: (3-2*x)/(1-x)^5.

a(n) = (n+12)*binomial(n+3, 3)/4 = 3*b(n)-2*b(n-1), with b(n) = binomial(n+4, 4); cf. A000332.

a(n) = Sum_{k=1..n} Sum_{i=1..k} i*(n-k+3), with offset 1. - Wesley Ivan Hurt, Sep 25 2013

From Amiram Eldar, Oct 21 2025: (Start)

Sum_{n>=0} 1/a(n) = 541091/1143450.

Sum_{n>=0} (-1)^n/a(n) = 160*log(2)/33 - 3526997/1143450. (End)

Maple

A095661:=n->(n+12)*binomial(n+3, 3)/4; seq(A095661(k), k=0..50); # Wesley Ivan Hurt, Oct 10 2013

Mathematica

Table[(n+12)Binomial[n+3, 3]/4, {n, 0, 50}] (* Wesley Ivan Hurt, Oct 10 2013 *)

Crossrefs

Partial sums of A006503.

Cf. A000332, A095660, A213550.

Sequence in context: A154154 A281868 A137976 * A058214 A108480 A322187

Adjacent sequences: A095658 A095659 A095660 * A095662 A095663 A095664

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 11 2004

Status

approved