A228124 - OEIS

%I #22 Jul 29 2015 11:20:57

%S 1,14,30,91,140,285,385,650,819,1240,1496,2109,2470,3311,3795,4900,

%T 5525,6930,7714,9455,10416,12529,13685,16206,17575,20540,22140,25585,

%U 27434,31395,33511,38024,40425,45526,48230,53955,56980,63365,66729,73810,77531,85344

%N Number of blocks in a Steiner Quadruple System of order A047235(n+1).

%C For order v, the number of blocks is v*(v-1)*(v-2)/24.

%H Colin Barker, <a href="/A228124/b228124.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).

%F a(n) = (n*(1+3*n)*(1+3*(-1)^n+6*n))/16.

%F a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7).

%F G.f.: x*(x^5+4*x^4+22*x^3+13*x^2+13*x+1) / ((x-1)^4*(x+1)^3).

%e For n=3, A047235(n+1)=10 and the number of blocks in SQS(10) is 30.

%t LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,14,30,91,140,285,385},50] (* _Harvey P. Dale_, Jul 29 2015 *)

%o (PARI) Vec(x*(x^5+4*x^4+22*x^3+13*x^2+13*x+1)/((x-1)^4*(x+1)^3) + O(x^100))

%K nonn,easy

%O 1,2

%A _Colin Barker_, Aug 11 2013