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

0,2

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).

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.

Example

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)
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The ninth powers:    1, 512, 19683, 262144, 1953125, ...  (A001017)
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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 *)

Prog

(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

Crossrefs

Cf. A001017, A007487, A022525, A253637, A255179, A255182.

Sequence in context: A110025 A059763 A031421 * A126438 A126582 A062905

Adjacent sequences: A255180 A255181 A255182 * A255184 A255185 A255186

Keyword

nonn,easy

Author

Luciano Ancora, Mar 18 2015

Extensions

Edited by Bruno Berselli, Mar 20 2015

Status

approved