A063916 G.f.: (1 + Sum_{ i >= 0 } 2^i*x^(2^(i+1)-1)) / (1-x)^3.

1, 4, 9, 18, 31, 48, 69, 98, 135, 180, 233, 294, 363, 440, 525, 626, 743, 876, 1025, 1190, 1371, 1568, 1781, 2010, 2255, 2516, 2793, 3086, 3395, 3720, 4061, 4434, 4839, 5276, 5745, 6246, 6779, 7344, 7941, 8570, 9231, 9924, 10649, 11406, 12195, 13016, 13869

Offset: 0

Author

N. J. A. Sloane, Sep 01 2001

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Partial sums of A063915.

Programs

Maple

b:= proc(n) option remember; `if`(n<0, 0, 1+
     (t-> 2*(b(floor(t))+b(ceil(t))))(n/2-1))
    end:
a:= proc(n) option remember; `if`(n<0, 0, b(n)+a(n-1)) end:
seq(a(n), n=0..55);  # Alois P. Heinz, Jul 10 2019

Mathematica

b[n_] := b[n] = If[EvenQ[n], 2b[n/2] + 2b[n/2-1], 4b[(n-1)/2]]+1;
b[0] = 0; b[1] = 1; b[2] = 3;
b /@ Range[100] // Accumulate (* Jean-François Alcover, Nov 09 2020 *)

Extensions

More terms from Ralf Stephan, Sep 15 2003