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%I #27 Jan 27 2022 20:49:35
%S 0,2025,24502500,249500250000,2499500025000000,24999500002500000000,
%T 249999500000250000000000,2499999500000025000000000000,
%U 24999999500000002500000000000000,249999999500000000250000000000000000,2499999999500000000025000000000000000000
%N a(n) = Sum_{i=0..10^n-1} i^3.
%C 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.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11100,-11100000,1000000000).
%F a(n) = 10^(2n) * (10^n-1)^2 / 4 = A037182(n)^2.
%F a(n) = A000217(10^n-1)^2.
%F a(n) = A038544(n) - 10^(3*n).
%e a(1) = Sum_{i=0..9} i^3 = (Sum_{i=0..9} i)^2 = 2025.
%t a[n_] := (10^n*(10^n - 1)/2)^2; Array[a, 11, 0] (* _Amiram Eldar_, Jan 20 2022 *)
%o (PARI) a(n) = my(x=10^n-1); (x*(x+1)/2)^2; \\ _Michel Marcus_, Jan 22 2022
%Y Cf. A000217, A037156, A037182, A038544, A238237.
%K nonn,base,easy
%O 0,2
%A _Bernard Schott_, Jan 20 2022