A286314 Number of representations of 10^n as sum of 6 triangular numbers.

6, 231, 20400, 2003001, 200045352, 20000567352, 1959085094400, 200000030000001, 20118337236261000, 1999999999505541852, 200000000030000000001, 19994255180823548693100, 1959183673472326530612252, 200000000000105810631542400, 20118343160415860069040000000

Offset: 0

Author

Seiichi Manyama, May 06 2017

Keywords

• nonn

Comments

a(n) is nearly 2*10^(2*n) because a(n) is almost (4*10^n+3)^2 / 8.

Examples

			a(0) = 1/8 * (Sum_{d|7, d == 3 mod 4} d^2 - Sum_{d|7, d == 1 mod 4} d^2) = 1/8 * (7^2 - 1^2) = 6.
a(1) = 1/8 * (Sum_{d|43, d == 3 mod 4} d^2 - Sum_{d|43, d == 1 mod 4} d^2) = 1/8 * (43^2 - 1^2) = 231.
a(2) = 1/8 * (Sum_{d|403, d == 3 mod 4} d^2 - Sum_{d|403, d == 1 mod 4} d^2) = 1/8 * (403^2 + 31^2 - 13^2 - 1^2) = 20400.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..17

Crossrefs

Cf. A008440, A286315.

Formula

a(n) = A008440(10^n).

a(n) = 1/8 * (Sum_{d|4*10^n+3, d == 3 mod 4} d^2 - Sum_{d|4*10^n+3, d == 1 mod 4} d^2).

Extensions

More terms from Seiichi Manyama, May 07 2017