A095668 Sixth column (m=5) of (1,4)-Pascal triangle A095666.

4, 21, 66, 161, 336, 630, 1092, 1782, 2772, 4147, 6006, 8463, 11648, 15708, 20808, 27132, 34884, 44289, 55594, 69069, 85008, 103730, 125580, 150930, 180180, 213759, 252126, 295771, 345216, 401016, 463760, 534072, 612612, 700077, 797202, 904761

Offset: 0

Author

Wolfdieter Lang, Jun 11 2004

Keywords

• nonn
• easy

Comments

If Y is a 4-subset of an n-set X, then, for n >= 8, a(n-8) is the number of 5-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 08 2007

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A000389, A095666.

Cf. A000217, A055999.

Programs

Magma

[(n+20)*Binomial(n+4, 4)/5: n in [0..30]]; // G. C. Greubel, Nov 25 2017

Maple

A095668:=n->(n+20)*binomial(n+4, 4)/5: seq(A095668(n), n=0..80); # Wesley Ivan Hurt, Nov 25 2017

Mathematica

Table[(n + 20)*Binomial[n + 4, 4]/5, {n, 0, 50}] (* G. C. Greubel, Nov 25 2017 *)

PARI

for(n=0,30, print1((n+20)*binomial(n+4, 4)/5, ", ")) \\ G. C. Greubel, Nov 25 2017

Formula

G.f.: (4-3*x)/(1-x)^6.

a(n) = (n+20)*binomial(n+4, 4)/5.

a(n) = 4*b(n) - 3*b(n-1), with b(n) = binomial(n+5, 5) = A000389(n+5, 5).

E.g.f.: (480 + 2040*x + 1680*x^2 + 440*x^3 + 40*x^4 + x^5)*exp(x)/120. - G. C. Greubel, Nov 25 2017

a(n) = Sum_{i=0..n+1} A000217(i)*A055999(n+2-i). - Bruno Berselli, Mar 05 2018