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Search: id:A134163
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| A134163 |
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a(n) = 1 + 12n + 81n^3 + n(105n+ 81n^3)/2. |
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+0
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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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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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 (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
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MATHEMATICA
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1) Table[(3(3n + 1)^4 + 6(3n + 1)^3 - (3n + 1)^2 - 4 (3n + 1) + 2)/6, {n, 0, 100}] 2) Table[Sum[k^7, {k, 1, 3n + 1}]/Sum[k^3, {k, 1, 3n + 1}], {n, 0, 100}] (*Artur Jasinski*)
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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 this_sequence A030536 A143661 A070257
Adjacent sequences: A134160 A134161 A134162 this_sequence A134164 A134165 A134166
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Oct 10 2007
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