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 A296851 Decimal expansion of limiting power-ratio for A296849; see Comments. 2
 2, 2, 8, 3, 3, 7, 8, 4, 1, 4, 0, 4, 2, 9, 9, 5, 1, 2, 2, 7, 9, 9, 6, 6, 6, 6, 0, 0, 3, 9, 8, 6, 7, 8, 7, 4, 9, 0, 8, 9, 9, 2, 8, 2, 7, 5, 3, 5, 4, 8, 8, 4, 9, 3, 7, 3, 9, 1, 2, 5, 0, 6, 6, 3, 2, 3, 2, 0, 7, 6, 1, 0, 5, 2, 0, 8, 9, 0, 2, 7, 0, 6, 1, 3, 5, 8 (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 = A296849, we have g = 1+ sqrt(2). See the guide at A296469 for related sequences. LINKS EXAMPLE limiting power-ratio = 2.283378414042995122799666600398678749089... MATHEMATICA a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4; b[2] = 5; a[n_] := a[n] = 2 a[n - 1] + a[n - 2] + b[n]; j = 1; While[j < 8, k = a[j] - j - 1; While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++]; u = Table[a[n], {n, 0, k}]; (* A296849 *) z = 1700; r = 1 + Sqrt[2]; h = Table[N[a[n]/r^n, z], {n, 0, z}]; StringJoin[StringTake[ToString[h[[z]]], 41], "..."] Take[RealDigits[Last[h], 10][[1]], 120] (* A296851 *) CROSSREFS Cf. A296849, A296850. Sequence in context: A121860 A283990 A021442 * A166853 A143440 A093731 Adjacent sequences:  A296848 A296849 A296850 * A296852 A296853 A296854 KEYWORD nonn,easy,cons AUTHOR Clark Kimberling, Jan 13 2018 STATUS approved

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Last modified December 8 12:07 EST 2019. Contains 329862 sequences. (Running on oeis4.)