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

1,2

Comments

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

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).

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).

Example

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

Mathematica

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

Prog

(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))

Crossrefs

Sequence in context: A308312 A101960 A075208 * A293391 A015222 A054103

Adjacent sequences: A228121 A228122 A228123 * A228125 A228126 A228127

Keyword

nonn,easy

Author

Colin Barker, Aug 11 2013

Status

approved