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

Author

Seiichi Manyama, Jul 28 2024

Keywords

• nonn

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.

Crossrefs

Cf. A000005, A000203, A001157, A189835.

Programs

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)))));

Formula

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