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A255178 Second differences of eighth powers (A001016). 5
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 (list; graph; refs; listen; history; text; internal format)
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)

----------------------------------------------------------------------

The eighth powers:   1, 256, 6561, 65536, 390625, ... (A001016)

----------------------------------------------------------------------

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}]]

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: A062664 A258696 A158249 * 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

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Last modified May 25 00:59 EDT 2019. Contains 323534 sequences. (Running on oeis4.)