A350869 a(n) = Sum_{i=0..10^n-1} i^3.

0, 2025, 24502500, 249500250000, 2499500025000000, 24999500002500000000, 249999500000250000000000, 2499999500000025000000000000, 24999999500000002500000000000000, 249999999500000000250000000000000000, 2499999999500000000025000000000000000000

Offset: 0

Author

Bernard Schott, Jan 20 2022

Keywords

• nonn
• base
• easy

Comments

These terms k = x.y satisfy 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.

Examples

			a(1) = Sum_{i=0..9} i^3 = (Sum_{i=0..9} i)^2 = 2025.
		

Links

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

Crossrefs

Cf. A000217, A037156, A037182, A038544, A238237.

Programs

Mathematica

a[n_] := (10^n*(10^n - 1)/2)^2; Array[a, 11, 0] (* Amiram Eldar, Jan 20 2022 *)

PARI

a(n) = my(x=10^n-1); (x*(x+1)/2)^2; \\ Michel Marcus, Jan 22 2022

Formula

a(n) = 10^(2n) * (10^n-1)^2 / 4 = A037182(n)^2.

a(n) = A000217(10^n-1)^2.

a(n) = A038544(n) - 10^(3*n).