A280220 a(1) = 1, a(n+1) is the numerator of n-th partial fraction of the continued fraction [1; 4, 16, 64, ..., 4^n].

1, 5, 81, 5189, 1328465, 1360353349, 5572008645969, 91291791015909445, 5982898821590650033489, 1568381028778351153394849861, 1644566705638271237843748737881425, 6897812711726991987001765057444407253061, 115726093792191122162903443021235072225308939601

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..58

Formula

a(n) = 4^(n-1)*a(n-1) + a(n-2).

Example

G.f. = x + 5*x^2 + 81*x^3 + 5189*x^4 + 1328465*x^5 + 1360353349*x^6 + ...
a(3) = 81, the numerator of 1 + 1/(4 + 1/16) = 81/65.

Mathematica

f[n_] := Numerator[ FromContinuedFraction[ Reverse[4^Range[0, n -1]] ]]; Array[f, 12] (* Robert G. Wilson v, Dec 29 2016 *)

Crossrefs

Denominators are in A015475.

Cf. A061377, A280219.

Sequence in context: A165435 A197443 A337852 * A280675 A209102 A274388

Adjacent sequences: A280217 A280218 A280219 * A280221 A280222 A280223

Keyword

nonn,frac

Author

Seiichi Manyama, Dec 29 2016

Status

approved