

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
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OFFSET

0,1


COMMENTS

If Y is a 3subset of an nset X then, for n>=8, a(n8) is the number of 6subsets 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.: (32*x)/(1x)^7.
a(n)= binomial(n+5, 5)*(n+18)/6 = 3*b(n)2*b(n1), 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(n1)21*a(n2)+35*a(n3)35*a(n4)+21*a(n5)7*a(n6)+a(n7).  Harvey P. Dale, Mar 30 2014


MATHEMATICA

CoefficientList[Series[(32x)/(1x)^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



