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 A106607 Expansion of (1+t^3)^2/((1-t)*(1-t^2)^2*(1-t^4)). 2
 1, 1, 3, 5, 9, 13, 20, 28, 39, 51, 67, 85, 107, 131, 160, 192, 229, 269, 315, 365, 421, 481, 548, 620, 699, 783, 875, 973, 1079, 1191, 1312, 1440, 1577, 1721, 1875, 2037, 2209, 2389, 2580, 2780, 2991, 3211, 3443, 3685, 3939, 4203, 4480, 4768, 5069, 5381, 5707, 6045 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Molien series for 5-dimensional group of order 8. For of each of the quadrisections the n-th term is a polynomial in n of degree 3. - Ralf Stephan, Nov 16 2010 Number of non-isomorphic 3 X 3 nonnegative integer matrices with all row and column sums equal to n up to permutations of rows and columns. - Andrew Howroyd, Apr 08 2020 LINKS S. Ling and P. Solé, Type II Codes over F_4 + u F_4, European J. Combinatorics, 22 (2001), 983-997. Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1,-3,3,-1). FORMULA G.f.: (x^2-x+1)^2 / ( (1+x)*(x^2+1)*(x-1)^4 ). - R. J. Mathar, Dec 18 2014 a(n) = (4*n^3+18*n^2+56*n+3*(9*(-1)^n+(2-2*i)*(-i)^n+(2+2*i)*i^n+19))/96 where i is the imaginary unit. - Colin Barker, Feb 08 2016 EXAMPLE The a(4) = 9 symmetric matrices are:   [0 0 4]  [0 1 3]  [0 1 3]  [0 2 2]  [0 2 2]   [0 4 0]  [1 2 1]  [1 3 0]  [2 0 2]  [2 1 1]   [4 0 0]  [3 1 0]  [3 0 1]  [2 2 0]  [2 1 1] .   [1 1 2]  [1 0 3]  [1 1 2]  [2 0 2]   [1 2 1]  [0 4 0]  [1 3 0]  [0 4 0]   [2 1 1]  [3 0 1]  [2 0 2]  [2 0 2] MAPLE (1+t^3)^2/((1-t)*(1-t^2)^2*(1-t^4)); seq(coeff(series(%, t, n+1), t, n), n=0..60); PROG (PARI) a(n) = i=I; (4*n^3+18*n^2+56*n+3*(9*(-1)^n+(2-2*i)*(-i)^n+(2+2*i)*i^n+19))/96 \\ Colin Barker, Feb 08 2016 CROSSREFS Row n=3 of A333737. Cf. A100779. Sequence in context: A108754 A033499 A267262 * A305082 A007042 A178415 Adjacent sequences:  A106604 A106605 A106606 * A106608 A106609 A106610 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, May 12 2005 STATUS approved

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Last modified January 27 22:40 EST 2021. Contains 340489 sequences. (Running on oeis4.)