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Search: id:A105780
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| A105780 |
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Coefficients of the A-Rogers mod 14 identity. |
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+0
3
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| 1, 1, 2, 3, 5, 7, 10, 14, 19, 26, 35, 46, 61, 79, 102, 131, 167, 211, 266, 333, 415, 515, 636, 782, 959, 1171, 1425, 1729, 2091, 2521, 3033, 3637, 4351, 5193, 6183, 7345, 8708, 10301, 12161, 14331, 16856, 19789, 23195, 27139, 31703, 36978, 43063
(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, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, ...]. - Michael Somos Sep 21 2005
G.f.: Product_{k>0} (1-x^(14k))(1-x^(14k-6))(1-x^(14k-8))/(1-x^k) = Sum_{k>=0} x^(k^2)/(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 + 5*q^4 + 7*q^5 + 10*q^6 + 14*q^7 + 19*q^8 + 26*q^9 + 35*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, 1, 1, 0, 1, 0, 1, 1, 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. A105781, A105782.
Adjacent sequences: A105777 A105778 A105779 this_sequence A105781 A105782 A105783
Sequence in context: A023026 A096778 A102108 this_sequence A001522 A054405 A116634
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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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