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A280219 a(1) = 1, a(n+1) is the numerator of n-th partial fraction of the continued fraction [1; 3, 9, 27, ..., 3^n]. 4

%I #25 Dec 31 2016 03:13:05

%S 1,4,37,1003,81280,19752043,14399320627,31491333963292,

%T 206614656532479439,4066796316020126761129,

%U 240140255871287121650385760,42540125910897696055021012987849,22607567054453522745047709284925846169,36043764129000043869363596706325850854686436,172396206472341818392860586297603696245873653954653

%N a(1) = 1, a(n+1) is the numerator of n-th partial fraction of the continued fraction [1; 3, 9, 27, ..., 3^n].

%H Seiichi Manyama, <a href="/A280219/b280219.txt">Table of n, a(n) for n = 1..65</a>

%F a(n) = 3^(n-1)*a(n-1) + a(n-2).

%e G.f. = x + 4*x^2 + 37*x^3 + 1003*x^4 + 81280*x^5 + 19752043*x^6 + ...

%e a(3) = 37, the numerator of 1 + 1/(3 + 1/9) = 37/28.

%t f[n_] := Numerator[ FromContinuedFraction[ Reverse[3^Range[0, n -1]] ]]; Array[f, 14] (* _Robert G. Wilson v_, Dec 30 2016 *)

%Y Denominators are in A015474.

%Y Cf. A061377, A280220.

%K nonn,frac

%O 1,2

%A _Seiichi Manyama_, Dec 29 2016

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