A029941 Number of symmetric types of (4,2n)-hypergraphs under action of complementing group C(4,2).

1, 15, 50, 225, 590, 1485, 3130, 6435, 11931, 21450, 36220, 59670, 94140, 145350, 217500, 319770, 458981, 648945, 900350, 1233375, 1663850, 2220075, 2924870, 3817125, 4928511, 6310980, 8007640, 10086780, 12605560, 15651900, 19300440, 23662980, 28835081

Offset: 0

Author

Vladeta Jovovic, Jul 13 2000

Keywords

• nonn
• easy

Comments

The first g.f. gives a 0 between each two terms of the sequence - Colin Barker, Jul 12 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4,-4,11,-8,0,8,-10,0,8,0,-10,8,0,-8,11,-4,-4,4,-1).

Crossrefs

Cf. A051502.

Programs

Mathematica

CoefficientList[Series[(9 x^12 - 21 x^11 + 26 x^10 + 121 x^9 - 149 x^8 + 132 x^7 + 20 x^6 + 68 x^5 - 61 x^4 + 89 x^3 - 6 x^2 + 11 x + 1)/((x - 1)^8 (x + 1)^4 (x^2 + 1)^2 (x^4 + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 19 2013 *)
LinearRecurrence[{4,-4,-4,11,-8,0,8,-10,0,8,0,-10,8,0,-8,11,-4,-4,4,-1},{1,15,50,225,590,1485,3130,6435,11931,21450,36220,59670,94140,145350,217500,319770,458981,648945,900350,1233375},40] (* Harvey P. Dale, Aug 14 2021 *)

Formula

G.f.: (30/(1-x^2)^8-70/(1-x^4)^4+120/(1-x^8)^2-64/(1-x^16))/16.

G.f.: (9*x^12 -21*x^11 +26*x^10 +121*x^9 -149*x^8 +132*x^7 +20*x^6 +68*x^5 -61*x^4 +89*x^3 -6*x^2 +11*x +1) / ((x-1)^8 *(x+1)^4 *(x^2+1)^2 *(x^4+1)). - Colin Barker, Jul 12 2013

a(n) = 4*a(n-1)-4*a(n-2)-4*a(n-3)+11*a(n-4)-8*a(n-5)+8*a(n-7)-10*a(n-8)+8*a(n-10)-10*a(n-12)+8*a(n-13)-8*a(n-15)+11*a(n-16)-4*a(n-17)-4*a(n-18)+4*a(n-19)-a(n-20). - Wesley Ivan Hurt, May 24 2021

Extensions

More terms from James Sellers, Aug 08 2000

More terms from Colin Barker, Jul 12 2013