A280219 - OEIS

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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].

1, 4, 37, 1003, 81280, 19752043, 14399320627, 31491333963292, 206614656532479439, 4066796316020126761129, 240140255871287121650385760, 42540125910897696055021012987849, 22607567054453522745047709284925846169, 36043764129000043869363596706325850854686436, 172396206472341818392860586297603696245873653954653

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..65

FORMULA

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

EXAMPLE

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

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

MATHEMATICA

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