A140402 Expansion of x^4/((1-x)^2*(1-x^3)) + x^5/((1-x)*(1-x^2)*(1-x^5)).

0, 0, 0, 0, 1, 3, 4, 7, 9, 12, 16, 20, 24, 29, 34, 40, 46, 53, 59, 67, 75, 83, 92, 101, 110, 121, 131, 142, 153, 165, 177, 190, 203, 216, 230, 245, 259, 275, 290, 306, 323, 340, 357, 375, 393, 412, 431, 451, 470, 491, 512, 533, 555, 577, 599, 623, 646, 670, 694, 719, 744, 770

Offset

0,6

Links

Table of n, a(n) for n=0..61.

Guoce Xin, Constructing all magic squares of order three, Discrete Math., 308 (2008), 3393-3398.

Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,0,-1,-1,0,1)

Formula

a(n) = 13/60*n^2 - 3/5*n + O(1). - Charles R Greathouse IV, Jun 03 2026

Prog

(PARI) a(n)=(13*n^2-36*n+[0, 23, 20, -9, -4, 35, -12, 35, -4, -9, 20, 23, 0, 11, -4, 15, 8, 35, -24, 11, 20, 3, 20, 11, -24, 35, 8, 15, -4, 11][n%30+1])/60 \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Sequence in context: A369568 A248358 A244952 * A005539 A253060 A203623

Adjacent sequences: A140399 A140400 A140401 * A140403 A140404 A140405

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 20 2008

Status

approved