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 A296504 Decimal expansion of limiting power-ratio for A294553; see Comments. 3
 6, 1, 3, 6, 3, 8, 5, 5, 1, 8, 7, 0, 7, 8, 2, 2, 2, 2, 1, 7, 6, 8, 4, 1, 2, 7, 9, 0, 4, 4, 0, 0, 8, 9, 9, 6, 0, 0, 3, 7, 0, 4, 0, 0, 3, 1, 5, 5, 9, 4, 5, 8, 4, 1, 4, 2, 0, 8, 2, 2, 8, 2, 1, 3, 1, 8, 0, 0, 7, 5, 4, 2, 2, 5, 0, 2, 5, 0, 8, 5, 9, 0, 3, 1, 0, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Suppose that A = (a(n)), for n >= 0, is a sequence, and g is a real number such that a(n)/a(n-1) -> g. The limiting power-ratio for A is the limit as n->oo of a(n)/g^n, assuming that this limit exists. For A = A294553, we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See the guide at A296469 for related sequences. LINKS EXAMPLE limiting power-ratio = 6.136385518707822221768412790440089960037... MATHEMATICA a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4; a[n_] := a[n] = a[n - 1] + a[n - 2] + b[n - 1] + b[n - 2] - n; j = 1; While[j < 13, k = a[j] - j - 1; While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++]; Table[a[n], {n, 0, k}]; (* A294553 *) z = 2000; g = GoldenRatio; h = Table[N[a[n]/g^n, z], {n, 0, z}]; StringJoin[StringTake[ToString[h[[z]]], 41], "..."] Take[RealDigits[Last[h], 10][[1]], 120]   (* A296504 *) CROSSREFS Cf. A001622, A294553, A296469, A296503. Sequence in context: A321093 A219552 A296476 * A188859 A074584 A195478 Adjacent sequences:  A296501 A296502 A296503 * A296505 A296506 A296507 KEYWORD nonn,easy,cons AUTHOR Clark Kimberling, Apr 14 2018 STATUS approved

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Last modified April 1 03:08 EDT 2020. Contains 333155 sequences. (Running on oeis4.)