A307889 G.f. A(x) satisfies: A(x) = 1 + x*A(x^2)/(1 - x)^2.

1, 1, 2, 4, 6, 10, 14, 22, 30, 44, 58, 82, 106, 144, 182, 242, 302, 392, 482, 616, 750, 942, 1134, 1408, 1682, 2062, 2442, 2966, 3490, 4196, 4902, 5850, 6798, 8048, 9298, 10940, 12582, 14706, 16830, 19570, 22310, 25800, 29290, 33722, 38154, 43720, 49286, 56260, 63234, 71890, 80546

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Maple

N:=100: # to get a(1)..a(N)
A:= 1:
for iter from 1 do
  B:= convert(series(1 + x*subs(x=x^2, A)/(1-x)^2, x, N+1), polynom);
  if B = A then break fi;
  A:= B;
od:
seq(coeff(A, x, j), j=0..N); # Robert Israel, May 03 2019

Mathematica

terms = 50; A[_] = 0; Do[A[x_] = 1 + x A[x^2]/(1 - x)^2 + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]
a[0] = 1; a[1] = 1; a[2] = 1; a[n_] := a[n] = 2 a[n - 1] - a[n - 2] + a[Floor[n/2]]; Join[{1, 1}, Differences[Table[2 a[n + 1], {n, 50}]]]

Crossrefs

Cf. A001906, A040039, A298414.

Sequence in context: A048670 A371719 A333315 * A239951 A077625 A027383

Adjacent sequences: A307886 A307887 A307888 * A307890 A307891 A307892

Keyword

nonn

Author

Ilya Gutkovskiy, May 03 2019

Status

approved