A095671 Ninth column (m=8) of (1,4)-Pascal triangle A095666.

4, 33, 153, 525, 1485, 3663, 8151, 16731, 32175, 58630, 102102, 171054, 277134, 436050, 668610, 1001946, 1470942, 2119887, 3004375, 4193475, 5772195, 7844265, 10535265, 13996125, 18407025, 23981724, 30972348, 39674668, 50433900

Offset

0,1

Comments

If Y is a 4-subset of an n-set X then, for n>=11, a(n-11) is the number of 8-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 08 2007

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Formula

G.f.: (4-3*x)/(1-x)^9.

a(n) = 4*b(n)-3*b(n-1) =(n+32)*binomial(n+7, 7)/8, with b(n):=binomial(n+8, 8)=A000581(n+8, 8).

a(0)=4, a(1)=33, a(2)=153, a(3)=525, a(4)=1485, a(5)=3663, a(6)=8151, a(7)=16731, a(8)=32175, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)- 126*a(n-4)+ 126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Jul 07 2015

Mathematica

CoefficientList[Series[(4-3x)/(1-x)^9, {x, 0, 30}], x] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {4, 33, 153, 525, 1485, 3663, 8151, 16731, 32175}, 30] (* Harvey P. Dale, Jul 07 2015 *)

Prog

(Maxima) A095671(n):=(n+32)*binomial(n+7, 7)/8$
makelist(A095671(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */

Crossrefs

Sequence in context: A362820 A364946 A209034 * A278671 A273676 A013192

Adjacent sequences: A095668 A095669 A095670 * A095672 A095673 A095674

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 11 2004

Status

approved