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%I #10 Jul 31 2015 12:56:34
%S 3,19,70,196,462,966,1848,3300,5577,9009,14014,21112,30940,44268,
%T 62016,85272,115311,153615,201894,262108,336490,427570,538200,671580,
%U 831285,1021293,1246014,1510320,1819576,2179672,2597056,3078768,3632475
%N Seventh column (m=6) of (1,3)-Pascal triangle A095660.
%C If Y is a 3-subset of an n-set X then, for n>=8, a(n-8) is the number of 6-subsets of X having at most one element in common with Y. - _Milan Janjic_, Nov 23 2007
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F G.f.: (3-2*x)/(1-x)^7.
%F a(n)= binomial(n+5, 5)*(n+18)/6 = 3*b(n)-2*b(n-1), with b(n):=binomial(n+6, 6); cf. A000579.
%F a(0)=3, a(1)=19, a(2)=70, a(3)=196, a(4)=462, a(5)=966, a(6)=1848, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - _Harvey P. Dale_, Mar 30 2014
%t CoefficientList[Series[(3-2x)/(1-x)^7,{x,0,40}],x] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{3,19,70,196,462,966,1848},40] (* _Harvey P. Dale_, Mar 30 2014 *)
%Y Sixth column: A000574. Eighth column: A095663.
%K nonn,easy
%O 0,1
%A _Wolfdieter Lang_, Jun 11 2004
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