A115293 Row sums of correlation triangle for (1+x)^3/(1-x).

1, 8, 31, 80, 160, 272, 416, 592, 800, 1040, 1312, 1616, 1952, 2320, 2720, 3152, 3616, 4112, 4640, 5200, 5792, 6416, 7072, 7760, 8480, 9232, 10016, 10832, 11680, 12560, 13472, 14416, 15392, 16400, 17440, 18512, 19616, 20752, 21920, 23120, 24352

Offset: 0

Author

Paul Barry, Jan 19 2006

Keywords

• nonn
• easy

Comments

Row sums of number triangle A115292.

If Y_i (i=1,2,3,4,5) are 2-blocks of a (n+5)-set X then a(n-2) is the number of 7-subsets of X intersecting each Y_i (i=1,2,3,4,5). - Milan Janjic, Oct 28 2007

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000
• Milan Janjic, Two Enumerative Functions
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A115291, A115292, A262732.

Programs

Maple

seq(add(binomial(5,n-k)*binomial(k+2,k), k = 0..n), n = 0..40); # Peter Bala, Sep 26 2021

Mathematica

LinearRecurrence[{3,-3,1},{1,8,31,80,160,272},50] (* Harvey P. Dale, Dec 03 2018 *)

PARI

a(n) = sum(k = 0, n, binomial(5,n-k)*binomial(k+2,k)); \\ Michel Marcus, Oct 01 2021

Formula

G.f.: A(x) = (1+x)^5/(1-x)^3.

a(n) = Sum_{k = 0..n} Sum_{j = 0..n} [j<=k]*A115291(k-j)*[j<=n-k]*A115291(n-k-j).

From Peter Bala, Sep 26 2021: (Start)

a(n) = Sum_{k = 0..n} binomial(5,n-k)*binomial(k+2,k).

A262732(n) = [x^n] A(x)^n. (End)