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Search: id:A134161
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| A134161 |
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a(n) = 373 + 1947n + 3780n^2 + 3234n^3 + 1029n^4. |
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+0
5
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| 373, 10363, 61723, 210901, 539041, 1151983, 2180263, 3779113, 6128461, 9432931, 13921843, 19849213, 27493753, 37158871, 49172671, 63887953, 81682213, 102957643, 128141131, 157684261, 192063313, 231779263, 277357783, 329349241
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OFFSET
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0,1
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COMMENT
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A000540(n) is divisable by A000330(n) if and only n is congruent to {1,2,4,5} mod 7 (see A047380) A134158 is case when n is congruent to 1 mod 7 A134159 is case when n is congruent to 2 mod 7 A134160 is case when n is congruent to 4 mod 7 A134161 is case when n is congruent to 5 mod 7 A133180 is union of A134158 and A134159 and A134160 and A134161
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FORMULA
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a(n) = (3(7n + 5)^4 + 6(7n + 5)^3 - 3 (7n + 5) + 1)/7 a(n) = Sum[k^6]/Sum[k^2], {k, 1, 7n + 5}]
G.f.: -(373+8498*x+13638*x^2+2186*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(7n + 5)^4 + 6(7n + 5)^3 - 3 (7n + 5) + 1)/7, {n, 0, 100}] 2) Table[Sum[k^6, {k, 1, 7n + 5}]/Sum[k^2, {k, 1, 7n + 5}], {n, 0, 100}] (*Artur Jasinski*)
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CROSSREFS
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Cf. A000330, A000540, A119617, A134153, A134154, A133180, A134158, A134159, A134160.
Adjacent sequences: A134158 A134159 A134160 this_sequence A134162 A134163 A134164
Sequence in context: A004021 A133559 A023313 this_sequence A108844 A025336 A025328
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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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