A228124 Number of blocks in a Steiner Quadruple System of order A047235(n+1).
1, 14, 30, 91, 140, 285, 385, 650, 819, 1240, 1496, 2109, 2470, 3311, 3795, 4900, 5525, 6930, 7714, 9455, 10416, 12529, 13685, 16206, 17575, 20540, 22140, 25585, 27434, 31395, 33511, 38024, 40425, 45526, 48230, 53955, 56980, 63365, 66729, 73810, 77531, 85344
Offset: 1
Examples
For n=3, A047235(n+1)=10 and the number of blocks in SQS(10) is 30.
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
Programs
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Mathematica
LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,14,30,91,140,285,385},50] (* Harvey P. Dale, Jul 29 2015 *) -
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))
Formula
a(n) = (n*(1+3*n)*(1+3*(-1)^n+6*n))/16.
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).
G.f.: x*(x^5+4*x^4+22*x^3+13*x^2+13*x+1) / ((x-1)^4*(x+1)^3).
Comments