

A298172


Decimal expansion of limiting powerratio for A296776; see Comments.


3



1, 1, 6, 5, 8, 3, 7, 7, 4, 8, 5, 0, 5, 6, 4, 6, 6, 6, 8, 1, 7, 0, 8, 6, 8, 2, 6, 0, 6, 2, 9, 3, 9, 4, 9, 4, 7, 3, 9, 2, 0, 5, 5, 6, 7, 8, 1, 6, 7, 0, 6, 2, 8, 1, 8, 0, 6, 9, 4, 5, 7, 6, 0, 9, 0, 5, 4, 8, 1, 9, 3, 4, 6, 0, 0, 2, 0, 5, 9, 7, 2, 8, 1, 3, 5, 9
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OFFSET

2,3


COMMENTS

Suppose that A = (a(n)), for n >= 0, is a sequence, and g is a real number such that a(n)/a(n1) > g. The limiting powerratio for A is the limit as n>oo of a(n)/g^n, assuming that this limit exists. For A = A296776, we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See the guide at A296462 for related sequences.


LINKS

Table of n, a(n) for n=2..87.


EXAMPLE

limiting powerratio = 11.65837748505646668170868260629394947392...


MATHEMATICA

a[0] = 1; a[1] = 3; b[0] = 2; b[1] = 4; b[2] = 5;
a[n_] := a[n] = a[n  1] + a[n  2] + b[n] + 2 n;
j = 1; While[j < 16, 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}]; (* A296776 *)
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] (* A298172 *)


CROSSREFS

Cf. A001622, A296462, A296776.
Sequence in context: A147313 A242759 A021607 * A225113 A329247 A133618
Adjacent sequences: A298169 A298170 A298171 * A298173 A298174 A298175


KEYWORD

nonn,easy,cons


AUTHOR

Clark Kimberling, Feb 09 2018


STATUS

approved



