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A014095
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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).
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5
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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
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OFFSET
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0,3
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LINKS
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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 linear recurrences with constant coefficients, signature (4,-2,-12,17,8,-28,8,17,-12,-2,4,-1).
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FORMULA
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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(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); 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. - Harvey P. Dale, Nov 13 2013
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MAPLE
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(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]);
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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