A095662 Seventh column (m=6) of (1,3)-Pascal triangle A095660.

3, 19, 70, 196, 462, 966, 1848, 3300, 5577, 9009, 14014, 21112, 30940, 44268, 62016, 85272, 115311, 153615, 201894, 262108, 336490, 427570, 538200, 671580, 831285, 1021293, 1246014, 1510320, 1819576, 2179672, 2597056, 3078768, 3632475, 4266507, 4989894, 5812404

Offset

0,1

Comments

If Y is a 3-subset of an n-set X then, for n >= 8, a(n-8) is the number of 6-subsets of X having at most one element in common with Y. - Milan Janjic, Nov 23 2007

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: (3-2*x)/(1-x)^7.

a(n) = binomial(n+5, 5)*(n+18)/6 = 3*b(n)-2*b(n-1), with b(n) = binomial(n+6, 6); cf. A000579.

a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7) with a(0)=3, a(1)=19, a(2)=70, a(3)=196, a(4)=462, a(5)=966, a(6)=1848. - Harvey P. Dale, Mar 30 2014

From Amiram Eldar, Oct 21 2025: (Start)

Sum_{n>=0} 1/a(n) = 5179914863/12636143520.

Sum_{n>=0} (-1)^n/a(n) = 7104*log(2)/221 - 55573028221/2527228704. (End)

Mathematica

CoefficientList[Series[(3-2x)/(1-x)^7, {x, 0, 40}], x] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {3, 19, 70, 196, 462, 966, 1848}, 40] (* Harvey P. Dale, Mar 30 2014 *)

Crossrefs

Cf. A000574 (sixth column), A095663 (eighth column).

Cf. A000579, A095660.

Sequence in context: A211061 A059599 A183461 * A090698 A350713 A215802

Adjacent sequences: A095659 A095660 A095661 * A095663 A095664 A095665

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 11 2004

Status

approved