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A095662 Seventh column (m=6) of (1,3)-Pascal triangle A095660. 3
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 (list; graph; refs; listen; history; text; internal format)
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..32.

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(0)=3, a(1)=19, a(2)=70, a(3)=196, a(4)=462, a(5)=966, a(6)=1848, 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). - Harvey P. Dale, Mar 30 2014

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

Sixth column: A000574. Eighth column: A095663.

Sequence in context: A211061 A059599 A183461 * A090698 A215802 A202041

Adjacent sequences:  A095659 A095660 A095661 * A095663 A095664 A095665

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jun 11 2004

STATUS

approved

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Last modified December 3 23:53 EST 2020. Contains 338920 sequences. (Running on oeis4.)