A255178 Second differences of eighth powers (A001016).

1, 254, 6050, 52670, 266114, 963902, 2796194, 6927230, 15257090, 30683774, 57405602, 101263934, 170126210, 274309310, 427043234, 644975102, 948713474, 1363412990, 1919399330, 2652834494, 3606422402, 4830154814, 6382097570, 8329217150, 10748247554

Offset

0,2

Links

Luciano Ancora, Table of n, a(n) for n = 0..1000

Luciano Ancora, Sums of powers of positive integers and their recurrence relations, section 0.5.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: (1 + x)*(1 + 246*x + 4047*x^2 + 11572*x^3 + 4047*x^4 + 246*x^5 + x^6)/(1 - x)^7.

a(n) = 2*(28*n^6 + 70*n^4 + 28*n^2 + 1) for n>0, a(0)=1.

Example

Second differences:  1, 254, 6050, 52670, 266114, ... (this sequence)
First differences:   1, 255, 6305, 58975, 325089, ... (A022524)
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The eighth powers:   1, 256, 6561, 65536, 390625, ... (A001016)
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First partial sums:  1, 257, 6818, 72354, 462979, ... (A000542)
Second partial sums: 1, 258, 7076, 79430, 542409, ... (A253636)
Third partial sums:  1, 259, 7335, 86765, 629174, ... (A254642)
Fourth partial sums: 1, 260, 7595, 94360, 723534, ... (A254647)

Mathematica

Join[{1}, Table[2 (28 n^6 + 70 n^4 + 28 n^2 + 1), {n, 1, 30}]]
Join[{1}, Differences[Range[0, 30]^8, 2]] (* Harvey P. Dale, Aug 26 2024 *)

Prog

(Magma) [n eq 0 select 1 else 2*(28*n^6+70*n^4+28*n^2+1): n in [0..30]]; // Vincenzo Librandi, Mar 12 2015

Crossrefs

Cf. A000542, A001016, A022524, A253636, A254642, A254647, A255177.

Sequence in context: A258696 A158249 A366553 * A196738 A195859 A250566

Adjacent sequences: A255175 A255176 A255177 * A255179 A255180 A255181

Keyword

nonn,easy

Author

Luciano Ancora, Feb 21 2015

Extensions

Edited by Bruno Berselli, Mar 19 2015

Status

approved