A289246 Coefficients in the expansion of 1/Sum_{k >= 0} ([r*(k + 1)] + [s*(k + 1)]) * (-x)^k, where [ ] = floor, r = (1+sqrt(5))/2, s = 1/r.

1, 4, 11, 32, 94, 272, 786, 2272, 6564, 18962, 54780, 158254, 457174, 1320712, 3815354, 11022024, 31841080, 91984410, 265730044, 767656774, 2217652596, 6406486864, 18507440702, 53465396640, 154454021166, 446195972602, 1288997492332, 3723732703246

Offset

0,2

Comments

Conjecture: the sequence is strictly increasing.

Links

Table of n, a(n) for n=0..27.

Formula

G.f.: 1/Sum_{k >= 0} ([r*(k + 1)] + [s*(k + 1)]) * (-x)^k, where [ ] = floor, r = (1+sqrt(5))/2, s = 1/r.

Mathematica

r = GoldenRatio; s = 1/GoldenRatio;
CoefficientList[Series[1/Sum[(Floor[r*(k + 1)] + Floor[s*(k + 1)]) (-x)^k, {k, 0, 1000}], {x, 0, 50}], x]

Crossrefs

Cf. A078140.

Sequence in context: A052545 A183114 A183119 * A199109 A025268 A178520

Adjacent sequences: A289243 A289244 A289245 * A289247 A289248 A289249

Keyword

nonn,easy

Author

Clark Kimberling, Aug 09 2017

Status

approved