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 A104565 Reversion of Pell numbers A000129(n+1). 3
 1, -2, 3, -2, -6, 28, -61, 54, 158, -860, 2062, -2004, -5804, 33720, -84509, 86054, 247862, -1492908, 3838298, -4019452, -11537556, 71101832, -185868978, 198310460, 567902572, -3555617432, 9404104764, -10168382696, -29069700056, 184127171952, -491229517661 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: (sqrt(1+4*x+8*x^2)-1-2*x)/(2*x^2). a(n) = sum{k=0..floor(n/2), binomial(n, 2k)*C(k)*(-1)^(n-k)2^(n-2k)}, where C(n) is A000108. - Paul Barry, May 16 2005 G.f. 1/G(0) where G(k)=  1 + 2*x + x^2/G(k+1); (continued fraction, 1-step). - Sergei N. Gladkovskii, Aug 10 2012 G.f.: (2/W(0)-1)/x  where W(k)=  1 + 1/(1 + 2*x/(1 + 2*x/W(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Sep 21 2012 Conjecture: (n+2)*a(n) +2*(2*n+1)*a(n-1) +8*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 09 2012 G.f.: G(0)/x^2 - 1/x - 1/x^2 where G(k)=  1 + 2*x/(1 + 1/(1 + 2*x/G(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Nov 23 2012 G.f.: 1/(x^2*Q(0)) - 1/(x^2) - 1/x, where Q(k)= 1 - (4*k+1)*x*(1+2*x)/(k+1 - x*(1+2*x)*(2*k+2)*(4*k+3)/(2*x*(1+2*x)*(4*k+3) - (2*k+3)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 15 2013 Lim sup n->infinity |a(n)|^(1/n) = 2*sqrt(2). - Vaclav Kotesovec, Feb 08 2014 a(n) = (-2)^n*hypergeom([1/2-n/2,-n/2], [2], -1). - Vladimir Reshetnikov, Nov 07 2015 MAPLE a:= proc(n) a(n):= `if`(n<2, 1-3*n,       ((8-8*n)*a(n-2)-(4*n+2)*a(n-1))/(n+2))     end: seq (a(n), n=0..40);  # Alois P. Heinz, Nov 09 2012 MATHEMATICA CoefficientList[Series[(Sqrt[1+4*x+8*x^2]-1-2*x)/(2*x^2), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 08 2014 *) Table[(-2)^n Hypergeometric2F1[1/2-n/2, -n/2, 2, -1], {n, 0, 20}] (* Vladimir Reshetnikov, Nov 07 2015 *) PROG (Sage) def A104565_list(n):  # n>=1     T = [0]*(n+1); R = [1]     for m in (1..n-1):         a, b, c = 1, 0, 0         for k in range(m, -1, -1):             r = a - 2*b - c             if k < m : T[k+2] = u;             a, b, c = T[k-1], a, b             u = r         T[1] = u; R.append(u)     return R A104565_list(30)  # Peter Luschny, Nov 01 2012 CROSSREFS Sequence in context: A143806 A276551 A109878 * A144456 A262427 A266258 Adjacent sequences:  A104562 A104563 A104564 * A104566 A104567 A104568 KEYWORD easy,sign AUTHOR Paul Barry, Mar 15 2005 STATUS approved

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Last modified April 1 13:39 EDT 2020. Contains 333159 sequences. (Running on oeis4.)