A288237 Coefficients in the expansion of 1/([r]-[2*r]*x+[3*r]*x^2-...); [ ]=floor, r=sqrt(11/4).

1, 3, 5, 9, 17, 30, 52, 91, 160, 281, 493, 865, 1518, 2664, 4675, 8204, 14397, 25265, 44337, 77806, 136540, 239611, 420488, 737905, 1294933, 2272449, 3987870, 6998224, 12281027, 21551700, 37820597, 66370521, 116472145, 204394366, 358687108, 629451995

Offset: 0

Author

Clark Kimberling, Jul 11 2017

Keywords

• nonn
• easy

Comments

Conjecture: the sequence is strictly increasing.

Links

• Robert Israel, Table of n, a(n) for n = 0..4089

Crossrefs

Cf. A078140 (includes guide to related sequences).

Programs

Maple

N:= 100: # to get a(0)..a(N)
r:= sqrt(11/4):
G:= 1/add(floor((k+1)*r)*(-x)^k,k=0..N):
S:= series(G,x,N+1):
seq(coeff(S,x,j),j=0..N); # Robert Israel, Jul 13 2017

Mathematica

r = Sqrt[11/4];
u = 1000; (* # initial terms from given series *)
v = 100;  (* # coefficients in reciprocal series *)
CoefficientList[Series[1/Sum[Floor[r*(k + 1)] (-x)^k, {k, 0, u}], {x, 0, v}], x]

Formula

G.f.: 1/(Sum_{k>=0} [(k+1)*r]*(-x)^k), where r = sqrt(11/4) and [ ] = floor.