A375035 Number of representations of n as 2*w*x + x*y + y*z + z*u + u*x where w, x, y, z>0, u>=0 are integers.

0, 0, 0, 1, 1, 4, 3, 11, 4, 21, 10, 30, 15, 51, 14, 71, 28, 86, 36, 119, 36, 150, 55, 178, 59, 219, 68, 269, 91, 278, 105, 367, 110, 396, 116, 469, 153, 504, 162, 587, 190, 608, 210, 752, 199, 759, 253, 906, 261, 879, 296, 1085, 325, 1068, 322, 1249, 378, 1239, 406, 1466, 435, 1425, 431, 1695, 464

Offset

1,6

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

R. P. Agarwal, Lambert series and Ramanujan, Prod. Indian Acad. Sci. (Math. Sci.), v. 103, n. 3, 1993, pp. 269-293. see p. 275.

Formula

If n is an odd, a(n) = (sigma_2(n) + 4*sigma(n) - (4*n+1)*sigma_0(n))/8.

Prog

(PARI) a(n) = sum(w=1, n\2, sum(x=1, n\(2*w), sum(y=1, n\x, sum(z=1, n\y, sum(u=0, n\z, 2*w*x+x*y+y*z+z*u+u*x==n)))));

Crossrefs

Cf. A000005, A000203, A001157, A189835.

Sequence in context: A100492 A072183 A353341 * A346614 A370631 A370630

Adjacent sequences: A375032 A375033 A375034 * A375036 A375037 A375038

Keyword

nonn

Author

Seiichi Manyama, Jul 28 2024

Status

approved