A100779 -id:A100779 - cp's OEIS frontend

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

Offset: 0

N. J. A. Sloane, May 12 2005

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
Take the square spiral on the square grid, with cells on the spiral numbered starting at 1. Every time the spiral crosses the x- or y-axis, calculate the sum of the numbers on the intersection of the spiral and the axis. This produces the present sequence (see illustration). - Karl-Heinz Hofmann, Aug 14 2022

			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]

G. C. Greubel, Table of n, a(n) for n = 0..1000
S. Ling and P. Solé, Type II Codes over F_4 + u F_4, European J. Combinatorics, 22 (2001), pp. 983-997.
Karl-Heinz Hofmann, An alternative way to get the terms of A106607. Examples of a(1..18)
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1,-3,3,-1).

Row n=3 of A333737.

Cf. A100779.

(1+t^3)^2/((1-t)*(1-t^2)^2*(1-t^4));
seq(coeff(series(%,t,n+1), t,n), n=0..60);

LinearRecurrence[{3,-3,1,1,-3,3,-1}, {1,1,3,5,9,13,20}, 61] (* G. C. Greubel, Sep 08 2021 *)

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

def A106607_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x^3)^2/((1-x)*(1-x^2)^2*(1-x^4)) ).list()
A106607_list(60) # G. C. Greubel, Sep 08 2021

G.f.: (1-x+x^2)^2/( (1+x)*(1+x^2)*(1-x)^4 ). - R. J. Mathar, Dec 18 2014
a(n) = (4*n^3 +18*n^2 +56*n +3*(9*(-1)^n +2*(1-i)*(-i)^n +2*(1+i)*i^n +19))/96 where i is the imaginary unit. - Colin Barker, Feb 08 2016
E.g.f.: (1/48)*(6*(cos(x) - sin(x)) + p(x)*sinh(x) + (27 + p(x))*cosh(x)), where p(x) = 15 + 39*x + 15*x^2 + 2*x^3. - G. C. Greubel, Sep 08 2021

cp's OEIS Frontend

A106607 Expansion of (1+t^3)^2/((1-t)(1-t^2)^2(1-t^4)).

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