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

Author

Wolfdieter Lang, Jun 11 2004

Keywords

• nonn
• easy

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

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

Crossrefs

Ninth column: A095663.

Programs

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 *)

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.