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A255182
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Third differences of eighth powers (A001016).
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3
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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
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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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).
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FORMULA
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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.
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EXAMPLE
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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
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Join[{1, 253}, Table[84 (2 n - 1) (2 n^4 - 4 n^3 + 8 n^2 - 6 n + 3), {n, 2, 30}]]
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PROG
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(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
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CROSSREFS
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Cf. A000542, A001016, A022524, A254642, A255178, A255181.
Sequence in context: A225021 A242463 A271985 * A176087 A006060 A077695
Adjacent sequences: A255179 A255180 A255181 * A255183 A255184 A255185
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KEYWORD
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nonn,easy
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AUTHOR
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Luciano Ancora, Mar 18 2015
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EXTENSIONS
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Edited by Bruno Berselli, Mar 19 2015
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STATUS
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approved
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