0,2

Alois P. Heinz, Table of n, a(n) for n = 0..10000

J. A. De Loera, D. Haws, R. Hemmecke, P. Huggins, B. Sturmfels and R. Yoshida, Short Rational Functions for Toric Algebra and Applications J. Symbolic Computation 38 (2) 2004, 959.

Index entries for linear recurrences with constant coefficients, signature (3,1,-10,3,14,-6,-13,7,10,-10,-7,13,6,-14,-3,10,-1,-3,1).

G.f.:= r(t)/s(t), where

r = t^54+150*t^51+5837*t^48+63127*t^45+331124*t^42+1056374*t^39+2326380*t^36+3842273*t^33+5055138*t^30+5512456*t^27+5055138*t^24+3842273*t^21+2326380*t^18+1056374*t^15+331124*t^12+63127*t^9+5837*t^6+150*t^3+1 and

s = (t^3+1)^4*(t^12+t^9+t^6+t^3+1)*(1-t^3)^9*(t^6+t^3+1).

LinearRecurrence[{3, 1, -10, 3, 14, -6, -13, 7, 10, -10, -7, 13, 6, -14, -3, 10, -1, -3, 1}, {1, 153, 6297, 82161, 582377, 2823169, 10577681, 32908425, 88984025, 215645185, 478631121, 988480025, 1922282689, 3552547017, 6284626217, 10704205425, 17636581137, 28219457161, 43991281193, 66997065953, 99914018553, 146199131313, 210261368801, 297660801977}, 30] (* Harvey P. Dale, Nov 28 2025 *)

Cf. A111158.

Sequence in context: A184369 A073938 A278285 * A269664 A384357 A281857

Adjacent sequences: A111083 A111084 A111085 * A111087 A111088 A111089

nonn,easy

N. J. A. Sloane, Oct 12 2005

This paper also gives a g.f. for the number of 5 X 5 magic squares with magic sum n (A111158). - N. J. A. Sloane.

approved