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 A330638 a(n) = P(n)*a(n-1) + a(n-2), with a(0) = 0, a(1) = 1 where P(n) is the n-th Pell number. 1
 0, 1, 2, 11, 134, 3897, 272924, 46128053, 18820518548, 18538256897833, 44083993723565422, 253086226505245985535, 3507775143446703083080522, 117373664327956358368203332177, 9481679355248745685146904663002936, 1849164516374760291573731440270350925577 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The ratio of the ratios of the consecutive numbers of this sequence tends to the silver ratio (A014176 = 1 + sqrt(2)). This property can be proven. LINKS FORMULA a(n) = A000129(n)*a(n-1) + a(n-2) for n > 1. a(n)*a(n-2)/a(n-1)^2 ~ 1 + sqrt(2). a(n) ~ c * (1 + sqrt(2))^(n*(n+1)/2) / 2^(3*n/2), where c = 1.2795822677496757181586660872019163393334688780614201258263927413618707127... - Vaclav Kotesovec, Dec 29 2019 MATHEMATICA Nest[Append[#1, Fibonacci[#2, 2] #1[[-1]] + #1[[-2]] ] & @@ {#, Length@ #} &, {0, 1}, 14] (* Michael De Vlieger, Dec 22 2019 *) PROG (PARI) seq(n)={my(u=Vec(1/(1 - 2*x - x^2) + O(x^n)), v=vector(#u+1)); v[2]=1; for(n=2, #u, v[n+1] = u[n]*v[n] + v[n-1]); v} \\ Andrew Howroyd, Dec 22 2019 CROSSREFS Cf. A000129 (Pell numbers), A014176 (silver ratio), A135829. Sequence in context: A282855 A139387 A041725 * A296571 A077544 A087480 Adjacent sequences:  A330635 A330636 A330637 * A330639 A330640 A330641 KEYWORD nonn AUTHOR Archit Handa, Dec 22 2019 STATUS approved

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Last modified May 31 02:51 EDT 2020. Contains 334747 sequences. (Running on oeis4.)