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A096945 Eighth column of (1,5)-Pascal triangle A096940. 2
5, 36, 148, 456, 1170, 2640, 5412, 10296, 18447, 31460, 51480, 81328, 124644, 186048, 271320, 387600, 543609, 749892, 1019084, 1366200, 1808950, 2368080, 3067740, 3935880, 5004675, 6310980, 7896816, 9809888, 12104136, 14840320 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

If Y is a 5-subset of an n-set X then, for n>=11, a(n-11) is the number of 7-subsets of X having at most one element in common with Y. > - Milan Janjic, Dec 08 2007

LINKS

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

FORMULA

G.f.: (5-4*x)/(1-x)^8.

a(n)= (n+35)*binomial(n+6, 6)/7 = 5*b(n)-4*b(n-1), with b(n):=A000580(n+7)=binomial(n+7, 7).

a(0)=5, a(1)=36, a(2)=148, a(3)=456, a(4)=1170, a(5)=2640, a(6)=5412, a(7)=10296, a(n)=8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)- 28*a(n-6)+ 8*a(n-7)-a(n-8). - Harvey P. Dale, Aug 16 2014

MATHEMATICA

CoefficientList[Series[(5-4*x)/(1-x)^8, {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {5, 36, 148, 456, 1170, 2640, 5412, 10296}, 30] (* Harvey P. Dale, Aug 16 2014 *)

CROSSREFS

Seventh column: A096944; ninth column: A096946.

Sequence in context: A276249 A027765 A196481 * A063417 A109726 A272561

Adjacent sequences:  A096942 A096943 A096944 * A096946 A096947 A096948

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jul 16 2004

STATUS

approved

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Last modified December 5 18:32 EST 2021. Contains 349557 sequences. (Running on oeis4.)