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Search: id:A119372
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| A119372 |
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G.f. satisfies: A(x) = 1 + x*(1-x-x^2)*A(x) + x^2*(3+2*x)*A(x)^2. |
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+0
8
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| 1, 1, 3, 9, 30, 104, 374, 1380, 5197, 19893, 77170, 302716, 1198729, 4785455, 19238706, 77821522, 316506253, 1293489529, 5309112257, 21876225899, 90459484106, 375256749620, 1561259497099, 6513108751281, 27238006266620
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Equals diagonal and row sums of pendular trinomial triangle A119369. Also equals convolution of A119370 and A119371 (central terms of A119369).
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FORMULA
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G.f.: A(x) = (1-x+x^2+x^3 - sqrt( (1-x+x^2+x^3)^2 - 4*x^2*(3+2*x)) )/(2*x^2*(3+2*x)). G.f.: A(x) = B(x)/(1+x - x*B(x)) = B(x)*G(x), where B(x) is g.f. of A119370, G(x) is g.f. of A119371.
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PROGRAM
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(PARI) {a(n)=polcoeff(2/(1-x+x^2+x^3+sqrt((1-x+x^2+x^3)^2-4*x^2*(3+2*x)+x*O(x^n))), n)}
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CROSSREFS
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Cf. A119369, A119370, A119371, A119373, A119374, A119375, A119376.
Sequence in context: A148953 A148954 A148955 this_sequence A145268 A148956 A003409
Adjacent sequences: A119369 A119370 A119371 this_sequence A119373 A119374 A119375
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 17 2006
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