A095665 Tenth column (m=9) of (1,3)-Pascal triangle A095660.

3, 28, 145, 550, 1705, 4576, 11011, 24310, 50050, 97240, 179894, 319124, 545870, 904400, 1456730, 2288132, 3513917, 5287700, 7811375, 11347050, 16231215, 22891440, 31865925, 43826250, 59603700, 80219568, 106919868, 141214920

Offset

0,1

Comments

If Y is a 3-subset of an n-set X then, for n>=11, a(n-11) is the number of 9-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..27.

Index entries for linear recurrences with constant coefficients, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

Formula

a(n)= binomial(n+8, 8)*(n+27)/9 = 3*b(n)-2*b(n-1), with b(n):=binomial(n+9, 9); cf. A000582.

G.f.: (3-2*x)/(1-x)^10.

Mathematica

Table[Binomial[n+8, 8] (n+27)/9, {n, 0, 30}] (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {3, 28, 145, 550, 1705, 4576, 11011, 24310, 50050, 97240}, 30] (* Harvey P. Dale, Oct 13 2017 *)

Crossrefs

Ninth column: A095663.

Sequence in context: A053132 A316390 A048367 * A145346 A184440 A012762

Adjacent sequences: A095662 A095663 A095664 * A095666 A095667 A095668

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 11 2004

Status

approved