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A134159
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a(n) = 13 + 165 n + 756 n^2 + 1470 n^3 + 1029 n^4.
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6
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13, 3433, 31591, 130351, 370273, 846613, 1679323, 3013051, 5017141, 7885633, 11837263, 17115463, 23988361, 32748781, 43714243, 57226963, 73653853, 93386521, 116841271, 144459103, 176705713, 214071493, 257071531, 306245611
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OFFSET
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0,1
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COMMENTS
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A000540(n) is divisible 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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LINKS
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Table of n, a(n) for n=0..23.
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FORMULA
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a(n) = (3(7n + 2)^4 + 6(7n + 2)^3 - 3 (7n + 2) + 1)/7 a(n) = Sum[k^6]/Sum[k^2], {k, 1, 7n + 2}]
G.f.: -(13+3368*x+14556*x^2+6596*x^3+163*x^4)/(-1+x)^5. - R. J. Mathar, Nov 14 2007
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MATHEMATICA
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1) Table[(3(7n + 2)^4 + 6(7n + 2)^3 - 3 (7n + 2) + 1)/7, {n, 0, 100}] 2) Table[Sum[k^6, {k, 1, 7n + 2}]/Sum[k^2, {k, 1, 7n + 2}], {n, 0, 100}] (*Artur Jasinski*)
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CROSSREFS
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Cf. A000330, A000540, A119617, A134153, A134154, A133180, A134158, A134160, A134161.
Sequence in context: A220642 A159357 A221885 * A221851 A221924 A070905
Adjacent sequences: A134156 A134157 A134158 * A134160 A134161 A134162
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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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