A128787 n^2*8^n.
0, 8, 256, 4608, 65536, 819200, 9437184, 102760448, 1073741824, 10871635968, 107374182400, 1039382085632, 9895604649984, 92908732547072, 862017116176384, 7916483719987200, 72057594037927936, 650770146155036672
Offset: 0
Examples
a(1) = 1^2 * 8^1 = 1 * 8 = 8. a(2) = 2^2 * 8^2 = 4 * 64 = 256. a(3) = 3^2 * 8^3 = 9 * 512 = 4608.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (24,-192,512).
Programs
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Magma
[n^2*8^n: n in [0..20]]; // Vincenzo Librandi, Feb 06 2013
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Mathematica
LinearRecurrence[{24, -192, 512}, {0, 8, 256}, 30] (* or *) CoefficientList[Series[8 x (1 + 8 x)/((1 - 8 x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 06 2013 *) Table[n^2 8^n, {n, 0, 19}] (* Alonso del Arte, Feb 06 2013 *)
Formula
G.f.: 8*x*(1 + 8*x)/(1 - 8*x)^3. - Vincenzo Librandi, Feb 06 2013
a(n) = 24*a(n-1) - 192*a(n-2) + 512*a(n-3). - Vincenzo Librandi, Feb 06 2013
Comments