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A095671 Ninth column (m=8) of (1,4)-Pascal triangle A095666. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A152041 A041027 A209034 * A278671 A273676 A013192

Adjacent sequences:  A095668 A095669 A095670 * A095672 A095673 A095674

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jun 11 2004

STATUS

approved

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Last modified June 14 12:26 EDT 2021. Contains 345025 sequences. (Running on oeis4.)