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A296458 Decimal expansion of limiting power-ratio for A296278; see Comments. 1
1, 9, 0, 0, 6, 0, 7, 5, 3, 0, 9, 3, 3, 0, 1, 5, 2, 3, 8, 8, 6, 9, 6, 8, 0, 8, 3, 8, 2, 9, 4, 1, 3, 8, 5, 8, 9, 0, 0, 0, 5, 8, 2, 8, 5, 9, 6, 0, 5, 6, 9, 7, 6, 1, 7, 7, 8, 4, 8, 0, 3, 1, 4, 4, 0, 4, 3, 7, 0, 9, 1, 6, 2, 4, 3, 5, 8, 6, 4, 6, 6, 6, 1, 6, 1, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

3,2

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 = A296278 we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See A296425-A296434 for related ratio-sums and A296452-A296461 for related limiting power-ratios.

LINKS

Table of n, a(n) for n=3..88.

EXAMPLE

Limiting power-ratio = 190.0607530933015238869680838294138589000...

MATHEMATICA

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

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

j = 1; While[j < 12, k = a[j] - j - 1;

While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++];

Table[a[n], {n, 0, 15}]  (* A296278 *)

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] (* A296458 *)

CROSSREFS

Cf. A001622, A296278.

Sequence in context: A254968 A019940 A257435 * A199870 A132267 A021115

Adjacent sequences:  A296455 A296456 A296457 * A296459 A296460 A296461

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Dec 15 2017

STATUS

approved

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Last modified September 30 11:32 EDT 2020. Contains 337439 sequences. (Running on oeis4.)