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

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

Offset

0,2

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

Links

Table of n, a(n) for n=0..10.

Index entries for linear recurrences with constant coefficients, signature (11100,-11100000,1000000000).

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)

From Elmo R. Oliveira, Nov 19 2025: (Start)

G.f.: (1 - 8075*x + 3025000*x^2)/((1-100*x)*(1-1000*x)*(1-10000*x)).

E.g.f.: exp(100*x)*(1 + 2*exp(900*x) + exp(9900*x))/4.

a(n) = 11100*a(n-1) - 11100000*a(n-2) + 1000000000*a(n-3). (End)

Example

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

Prog

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

Crossrefs

Cf. A037156, A238237, A350869, A350870.

Sequence in context: A225996 A167044 A221249 * A252142 A031553 A031733

Adjacent sequences: A038541 A038542 A038543 * A038545 A038546 A038547

Keyword

easy,nonn

Author

Marvin Ray Burns

Extensions

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

Status

approved