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Search: id:A105781
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| A105781 |
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Coefficients of the B-Rogers mod 14 identity. |
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+0
3
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| 1, 1, 2, 3, 4, 6, 9, 12, 17, 23, 30, 40, 53, 68, 88, 113, 143, 181, 228, 284, 354, 439, 541, 665, 815, 993, 1208, 1465, 1769, 2132, 2563, 3070, 3671, 4379, 5209, 6185, 7329, 8663, 10223, 12041, 14153, 16609, 19459, 22755, 26571, 30979, 36059
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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Eric Weisstein's World of Mathematics, Rogers Mod 14 Identities
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FORMULA
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Euler transform of period 14 sequence [1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, ...]. - Michael Somos Sep 21 2005
G.f.: Product_{k>0} (1-x^(14k))(1-x^(14k-4))(1-x^(14k-10))/(1-x^k) = Sum_{k>=0} x^(k^2+k)/((1-x^(2k+1))Product_{j=1..k} (1-x^j)(1-x^(2j-1))) . - Michael Somos Sep 21 2005
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EXAMPLE
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1 + q + 2*q^2 + 3*q^3 + 4*q^4 + 6*q^5 + 9*q^6 + 12*q^7 + 17*q^8 + 23*q^9 + 30*q^10 + ...
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, polcoeff( 1/prod(k=1, n, 1-[0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1][k%14+1]*x^k, 1+x*O(x^n)), n))} /* Michael Somos Sep 21 2005 */
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CROSSREFS
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Cf. A105780, A105782.
Sequence in context: A013950 A018550 A035952 this_sequence A035958 A035965 A035973
Adjacent sequences: A105778 A105779 A105780 this_sequence A105782 A105783 A105784
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Apr 19, 2005
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