A255183 Third differences of ninth powers (A001017).
1, 509, 18150, 204630, 1225230, 4985070, 15717750, 41436870, 95750430, 200038110, 385991430, 698516790, 1199001390, 1968942030, 3113936790, 4768039590, 7098477630, 10310731710, 14653979430, 20426901270
Offset: 0
Examples
Third differences: 1, 509, 18150, 204630, 1225230, ... (this sequence) Second differences: 1, 510, 18660, 223290, 1448520, ... (A255179) First differences: 1, 511, 19171, 242461, 1690981, ... (A022525) --------------------------------------------------------------------- The ninth powers: 1, 512, 19683, 262144, 1953125, ... (A001017) ---------------------------------------------------------------------
Links
- Luciano Ancora, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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Magma
[1,509] cat [6*(84*n^6-252*n^5+630*n^4-840*n^3+756*n^2-378*n+85): n in [2..30]]; // Vincenzo Librandi, Mar 18 2015
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Mathematica
Join[{1, 509}, Table[6 (84 n^6 - 252 n^5 + 630 n^4 - 840 n^3 + 756 n^2 - 378 n + 85), {n, 2, 30}]] Join[{1,509},Differences[Range[0,20]^9,3]] (* Harvey P. Dale, Apr 24 2015 *)
Formula
G.f.: (1 + 502*x + 14608*x^2 + 88234*x^3 + 156190*x^4 + 88234*x^5 + 14608*x^6 + 502*x^7 + x^8)/(1 - x)^7.
a(n) = 6*(84*n^6 - 252*n^5 + 630*n^4 - 840*n^3 + 756*n^2 - 378*n + 85) for n>1, a(0)=1, a(1)=509.
Extensions
Edited by Bruno Berselli, Mar 20 2015