A286315 Number of representations of 10^n as sum of 8 triangular numbers.

8, 1332, 1030302, 1007141184, 1000302990372, 1000781337641904, 1000003970597090004, 1000751615026326041904, 1000203571630368710405892, 1004272191614371538730009600, 1000000970912716777250166728808, 1000834130646589459517111102258880

Offset: 0

Author

Seiichi Manyama, May 06 2017

Keywords

• nonn

Comments

a(n) is nearly 10^(3*n) because a(n) is almost (10^n+1)^3.

Examples

			a(0) = Sum_{d|2, 2/d == 1 mod 2} d^3 = 2^3 = 8.
a(1) = Sum_{d|11, 11/d == 1 mod 2} d^3 = 11^3 + 1^3 = 1332.
a(2) = Sum_{d|101, 101/d == 1 mod 2} d^3 = 101^3 + 1^3 = 1030302.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..18

Crossrefs

Cf. A007331, A062397 (10^n+1), A168575 ((10^n+1)^3), A286314.

Formula

a(n) = A007331(10^n + 1).

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