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A297013 Decimal expansion of limiting power-ratio for A297011; see Comments. 2
9, 1, 9, 4, 0, 1, 9, 8, 6, 4, 2, 9, 2, 6, 9, 6, 7, 5, 8, 3, 1, 3, 2, 7, 0, 0, 0, 4, 6, 1, 7, 4, 2, 5, 9, 6, 8, 8, 7, 7, 7, 0, 5, 4, 9, 1, 9, 4, 8, 8, 1, 0, 8, 7, 9, 8, 9, 8, 9, 6, 9, 5, 9, 7, 5, 2, 6, 5, 0, 6, 9, 1, 2, 7, 1, 5, 3, 0, 5, 0, 6, 9, 7, 2, 5, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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 = A297011, we have g = 1+ sqrt(2). See the guide at A296469 for related sequences.

LINKS

Table of n, a(n) for n=0..85.

EXAMPLE

limiting power-ratio = 0.919401986429269675831327000461742596887...

MATHEMATICA

a[0] = 3; a[1] = 5; b[0] = 1; b[1] = 2; b[2] = 4;

a[n_] := a[n] = 2 a[n - 1] + a[n - 2] - b[n];

j = 1; While[j < 9, 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}]; (* A297011 *)

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] (* A297013 *)

CROSSREFS

Cf. A297011.

Sequence in context: A230458 A246687 A021525 * A197724 A176518 A154697

Adjacent sequences:  A297010 A297011 A297012 * A297014 A297015 A297016

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Jan 13 2018

STATUS

approved

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Last modified October 17 12:25 EDT 2019. Contains 328112 sequences. (Running on oeis4.)