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Partial sums of A051923.
4

%I #18 Jun 13 2015 00:50:02

%S 1,10,52,192,570,1452,3300,6864,13299,24310,42328,70720,114036,178296,

%T 271320,403104,586245,836418,1172908,1619200,2203630,2960100,3928860,

%U 5157360,6701175,8625006,11003760,13923712,17483752,21796720,26990832,33211200,40621449

%N Partial sums of A051923.

%C If Y is a 3-subset of an n-set X then, for n>=9, a(n-9) is the number of 9-subsets of X having at least two elements in common with Y. - _Milan Janjic_, Nov 23 2007

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1)

%F a(n)=C(n+6, 6)*(3n+7)/7.

%F G.f.: (1+2*x)/(1-x)^8.

%t Table[Binomial[n+6, 6]*(3*n+7)/7, {n, 0, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 27 2012 *)

%Y Cf. A051923.

%Y Cf. A093560 ((3, 1) Pascal, column m=7).

%K easy,nonn

%O 0,2

%A _Barry E. Williams_, Dec 26 1999