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A255182 Third differences of eighth powers (A001016). 3
1, 253, 5796, 46620, 213444, 697788, 1832292, 4131036, 8329860, 15426684, 26721828, 43858332, 68862276, 104183100, 152733924, 217931868, 303738372, 414699516, 555986340, 733435164, 953587908, 1223732412, 1551942756, 1947119580, 2419030404, 2978349948 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

G.f.: (1 + 247*x + 4293*x^2 + 15619*x^3 + 15619*x^4 + 4293*x^5 + 247*x^6 + x^7)/(1 - x)^6.

a(n) = 84*(2*n - 1)*(2*n^4 - 4*n^3 + 8*n^2 - 6*n + 3) for n>1, a(0)=1, a(1)=253.

EXAMPLE

Third differences:   1, 253, 5796, 46620, 213444, ...  (this sequence)

Second differences:  1, 254, 6050, 52670, 266114, ...  (A255178)

First differences:   1, 255, 6305, 58975, 325089, ...  (A022524)

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The seventh powers:  1, 253, 5796, 46620, 213444, ...  (A001016)

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MATHEMATICA

Join[{1, 253}, Table[84 (2 n - 1) (2 n^4 - 4 n^3 + 8 n^2 - 6 n + 3), {n, 2, 30}]]

PROG

(MAGMA) [1, 253] cat [84*(2*n-1)*(2*n^4-4*n^3+8*n^2-6*n+3): n in [2..30]]; // Vincenzo Librandi, Mar 18 2015

CROSSREFS

Cf. A000542, A001016, A022524, A254642, A255178, A255181.

Sequence in context: A225021 A242463 A271985 * A176087 A006060 A077695

Adjacent sequences:  A255179 A255180 A255181 * A255183 A255184 A255185

KEYWORD

nonn,easy

AUTHOR

Luciano Ancora, Mar 18 2015

EXTENSIONS

Edited by Bruno Berselli, Mar 19 2015

STATUS

approved

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Last modified November 16 03:08 EST 2018. Contains 317252 sequences. (Running on oeis4.)