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A029941
Number of symmetric types of (4,2n)-hypergraphs under action of complementing group C(4,2).
1
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
0,2
COMMENTS
The first g.f. gives a 0 between each two terms of the sequence - Colin Barker, Jul 12 2013
LINKS
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).
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
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 *)
CROSSREFS
Cf. A051502.
Sequence in context: A134742 A318084 A191746 * A349817 A278909 A194851
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Jul 13 2000
EXTENSIONS
More terms from James A. Sellers, Aug 08 2000
More terms from Colin Barker, Jul 12 2013
STATUS
approved