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Search: id:A084605
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| A084605 |
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G.f.: 1/(1-2x-15x^2)^(1/2); also, a(n) is the central coefficient of (1+x+4x^2)^n. |
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+0
6
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| 1, 1, 9, 25, 145, 561, 2841, 12489, 60705, 281185, 1353769, 6418809, 30917041, 148331665, 716698425, 3462260265, 16786700865, 81464917185, 396215601225, 1929237099225, 9408084660945, 45928695279345, 224476389327705
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also number of paths from (0,0) to (n,0) using steps U=(1,1), H=(1,0) and D=(1,-1), the U (or D) steps come in four colors. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Mar 30 2008
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REFERENCES
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Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
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FORMULA
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E.g.f.: exp(x)*BesselI(0, 4*x). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 20 2003
a(n) is also the central coefficient of (4+x+x^2)^n; a(n)=sum_{k=0..n} 3^(n-k) C(n,k) T(k,n), where T(k,n) is the triangle of trinomial coefficients = Coefficient of x^n of (1+x+x^2)^k : A027907 - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Mar 30 2008
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PROGRAM
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(PARI) for(n=0, 30, t=polcoeff((1+x+4*x^2)^n, n, x); print1(t", "))
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CROSSREFS
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Cf. A002426, A084600-A084604, A084606-A084615.
Sequence in context: A108570 A092769 A139818 this_sequence A098773 A089998 A014728
Adjacent sequences: A084602 A084603 A084604 this_sequence A084606 A084607 A084608
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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), Jun 01 2003
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