A038544 a(n) = Sum_{i=0..10^n} i^3.

1, 3025, 25502500, 250500250000, 2500500025000000, 25000500002500000000, 250000500000250000000000, 2500000500000025000000000000, 25000000500000002500000000000000, 250000000500000000250000000000000000, 2500000000500000000025000000000000000000

Offset: 0

Author

Marvin Ray Burns

Keywords

• easy
• nonn

Comments

These terms k = x.y satisfy Diophantine equation x.y = (x+y)^2, when x and y have the same number of digits, "." means concatenation, and y may not begin with 0. So, this is a subsequence of A350870 and A238237. - Bernard Schott, Jan 20 2022

Examples

			a(1) = Sum_{i=0..10} i^3 = (Sum_{i=0..10} i)^2 = 3025.
		

Crossrefs

Cf. A037156, A238237, A350869, A350870.

Programs

PARI

sumcu(n) = for(x=0,n,y=10^x;z=y^2*(y+1)^2/4;(print1(z","))) \\ Cino Hilliard, Jun 18 2007

Formula

a(n) = (10^n+1)^2 * 10^(2*n) / 4.

From Bernard Schott, Jan 20 2022: (Start)

a(n) = A037156(n)^2.

a(n) = A350869(n) + 10^(3*n). (End)

Extensions

Edited by N. J. A. Sloane, Jul 02 2008 at the suggestion of R. J. Mathar