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Search: id:A025262
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| A025262 |
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a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 4. |
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+0
6
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| 1, 1, 1, 3, 8, 23, 68, 207, 644, 2040, 6558, 21343, 70186, 232864, 778550, 2620459, 8872074, 30195288, 103246502, 354508628, 1221846856, 4225644866, 14659644348, 51002664023, 177909901566, 622093882290, 2180123564130, 7656055966092
(list; graph; listen)
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OFFSET
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1,4
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LINKS
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M. Somos, Number Walls in Combinatorics.
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FORMULA
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G.f.: (1-sqrt(1-4x+4x^3))/2. Satisfies A(x)-A(x)^2=x-x^3 - Michael Somos, Aug 04, 2000.
Comment from Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 27 2008: Given an integer t >= 1 and initial values u = [a_0, a_1, ..., a_{t-1}], we may define an infinite sequence Phi(u) by setting a_n = a_{n-1} + a_0*a_{n-1} + a_1*a_{n-2} + ... + a_{n-2}*a_1 for n >= t. For example Phi([1]) is the Catalan numbers A000108. The present sequence is Phi([1,1,1]).
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PROGRAM
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(PARI) a(n)=polcoeff((1-sqrt(1-4*x+4*x^3+x*O(x^n)))/2, n)
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CROSSREFS
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A056010 is essentially a duplicate of this entry.
Sequence in context: A025578 A038151 A057198 this_sequence A056010 A002712 A005960
Adjacent sequences: A025259 A025260 A025261 this_sequence A025263 A025264 A025265
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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