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A134163
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a(n) = 1 + 12n + 81n^3 + n(105n+ 81n^3)/2.
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1
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1, 187, 1531, 5977, 16441, 36811, 71947, 127681, 210817, 329131, 491371, 707257, 987481, 1343707, 1788571, 2335681, 2999617, 3795931, 4741147, 5852761, 7149241, 8650027, 10375531, 12347137, 14587201, 17119051, 19966987, 23156281, 26713177
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OFFSET
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0,2
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COMMENTS
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A000541(n) is divisible by A000537(n) if and only n is congruent to 1 mod 3 (see A016777)
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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a(n) = (3(3n + 1)^4 + 6(3n + 1)^3 - (3n + 1)^2 - 4 (3n + 1) + 2)/6
a(n) = Sum[k^7]/Sum[k^3], {k, 1, 3n + 1}
G.f.: -(1+182*x+606*x^2+182*x^3+x^4)/(-1+x)^5. - R. J. Mathar, Nov 14 2007
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MATHEMATICA
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Table[(3(3n + 1)^4 + 6(3n + 1)^3 - (3n + 1)^2 - 4 (3n + 1) + 2)/6, {n, 0, 100}] (* or *) Table[Sum[k^7, {k, 1, 3n + 1}]/Sum[k^3, {k, 1, 3n + 1}], {n, 0, 100}]
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PROG
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(MAGMA) [1 + 12*n + 81*n^3 + n*(105*n+ 81*n^3)/2: n in [0..30]]; // Vincenzo Librandi, May 09 2011
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CROSSREFS
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Cf. A000537, A000541, A119617, A134153, A134154, A133180, A134158, A134159, A134160.
Sequence in context: A029556 A045224 A063346 * A030536 A222911 A143661
Adjacent sequences: A134160 A134161 A134162 * A134164 A134165 A134166
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski, Oct 10 2007
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STATUS
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approved
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