A255182 Third differences of eighth powers (A001016).

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

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