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A014095 Molien series for real extraspecial group 2^{1+2*3} of degree 8 and order 128 formed from tensor products of Pauli matrices (0,1, 1,0) and (1,0, 0,-1). 5
1, 1, 15, 29, 135, 310, 870, 1830, 3993, 7535, 14157, 24427, 41535, 66812, 105740, 160956, 241281, 351405, 504811, 709225, 984423, 1342418, 1811250, 2408770, 3173625, 4131387, 5334057, 6817175, 8649279, 10878520, 13593624, 16858424, 20785985, 25459353 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

A. R. Calderbank, R. H. Hardin, E. M. Rains, P. W. Shor and N. J. A. Sloane, A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces, arXiv:math.CO/0208002, J. Algebraic Combinatorics, 9 (1999), 129-140.

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (4,-2,-12,17,8,-28,8,17,-12,-2,4,-1).

FORMULA

G.f.: (t^16-3*t^14+13*t^12-17*t^10+44*t^8-17*t^6+13*t^4-3*t^2+1) / (t^2+1)^4/(t-1)^8/(t+1)^8 (not simplified).

G.f.: (x^8-3*x^7+13*x^6-17*x^5+44*x^4-17*x^3+13*x^2-3*x+1) / ((x-1)^8*(x+1)^4). [Colin Barker, Jan 31 2013]

a(n) = n*(n+1)*(n+2)*(2*n*(n+2)*(2*n^2+4*n-1)-735*(-1)^n+915)/10080. [Bruno Berselli, Jan 31 2013]

a(0)=1, a(1)=1, a(2)=15, a(3)=29, a(4)=135, a(5)=310, a(6)=870, a(7)=1830, a(8)=3993, a(9)=7535, a(10)=14157, a(11)=24427, a(n)=4*a(n-1)- 2*a(n-2)- 12*a(n-3)+17*a(n-4)+8*a(n-5)-28*a(n-6)+8*a(n-7)+17*a(n-8)- 12*a(n-9)- 2*a(n-10)+4*a(n-11)-a(n-12). - Harvey P. Dale, Nov 13 2013

MAPLE

(t^16-3*t^14+13*t^12-17*t^10+44*t^8-17*t^6+13*t^4-3*t^2+1)/(t^2+1)^4/(t-1)^8/(t+1)^8:

seq(coeff(series(%, t, n+1), t, n), n=[(2*i)$i=0..30]);

MATHEMATICA

CoefficientList[Series[(x^8 - 3 x^7 + 13  x^6 - 17  x^5 + 44 x^4 - 17 x^3 + 13 x^2 - 3 x + 1)/((x-1)^8 (x+1)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 19 2013 *)

LinearRecurrence[{4, -2, -12, 17, 8, -28, 8, 17, -12, -2, 4, -1}, {1, 1, 15, 29, 135, 310, 870, 1830, 3993, 7535, 14157, 24427}, 40] (* Harvey P. Dale, Nov 13 2013 *)

PROG

(MAGMA) /* After Maple, for odd m: */ m:=67; R<t>:=PowerSeriesRing(Integers(), m); S:=Coefficients(R!((t^16-3*t^14+13*t^12-17*t^10+44*t^8-17*t^6+13*t^4-3*t^2+1)/(t^2+1)^4/(t-1)^8/(t+1)^8)); [S[2*i+1]: i in [0..m div 2]]; // Bruno Berselli, Jan 31 2013

CROSSREFS

Cf. A030533.

Sequence in context: A211324 A146427 A202512 * A192356 A196184 A201136

Adjacent sequences:  A014092 A014093 A014094 * A014096 A014097 A014098

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 14 12:19 EDT 2019. Contains 328006 sequences. (Running on oeis4.)