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Search: id:A122446
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| A122446 |
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G.f. satisfies: A(x) = 1 + x*A(x)^2 + 2*x^2*(A(x)^2 - A(x)); equals the base sequence of pendular trinomial triangle A122445. |
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8
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| 1, 1, 2, 7, 24, 88, 336, 1321, 5316, 21788, 90640, 381750, 1624592, 6975136, 30177056, 131428917, 575765820, 2535433668, 11216757104, 49829385786, 222193501760, 994153952528, 4461915817760, 20082611971226, 90625360612296
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Functional equation for the g.f. is derived from the recurrence of the pendular triangle A122445. Iterated convolutions of this sequence with the central terms (A122447) generates all diagonals of A122445. For example: A122448 = A122446 * A122447; A122449 = A122446^2 * A122447.
Diagonal sums of triangle T with T(n,k)=2^k*A133336(n,k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 10 2009]
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FORMULA
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G.f.: A(x) = (1+2x^2 - sqrt(1-4*x-4*x^2+4*x^4))/(2x(1+2x)).
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PROGRAM
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(PARI) {a(n)=polcoeff(2/(1+2*x^2+sqrt(1-4*x-4*x^2+4*x^4+x*O(x^n))), n)}
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CROSSREFS
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Cf. A122445, A122447, A122448, A122449, A122450, A122451, A122452.
Sequence in context: A150389 A104625 A151293 this_sequence A150390 A052705 A150391
Adjacent sequences: A122443 A122444 A122445 this_sequence A122447 A122448 A122449
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KEYWORD
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nonn,new
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Sep 07 2006
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