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Search: id:A086246
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| A086246 |
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Expansion of (1+x-sqrt(1-2x-3x^2))/2 in powers of x. |
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6
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| 0, 1, 1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019, 142547559, 400763223, 1129760415, 3192727797, 9043402501, 25669818476, 73007772802, 208023278209
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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A variant of the Motzkin numbers: see A001006 for the main entry.
Equals row sums of triangle A144218 starting with "1". [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 14 2008]
Starting (1, 1, 1,...) = inverse binomial transform of A014137: (1, 2, 4, 9, 23, 65,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 02 2009]
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FORMULA
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Series reversion of g.f. A(x) is -A(-x).
a(n)+a(n-1)=a(0)*a(n)+a(1)*a(n-1)+...+a(n)*a(0), n>2.
G.f. A(x) satisfies 0=f(x, A(x)) where f(x, y)=x-y-x*y+x^2+y^2.
G.f. A(x) satisfies 0=f(x, A(x)) where f(x, y)=(y^2-y^3)-(x^2+x^3).
G.f.: (1+x-sqrt(1-2x-3x^2))/2.
G.f. A(x) satisfies A(x) = x+C(xA(x)) where C(x) is g.f. for Catalan numbers A000108 (offset 1).
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PROGRAM
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(PARI) a(n)=polcoeff((1+x-sqrt(1-2*x-3*x^2+x*O(x^n)))/2, n)
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CROSSREFS
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a(n+2)=A001006(n).
Cf. A144218 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 14 2008]
A014137 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 02 2009]
Sequence in context: A094287 A094288 A166587 this_sequence A001006 A027057 A148071
Adjacent sequences: A086243 A086244 A086245 this_sequence A086247 A086248 A086249
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jul 13 2003
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