A113854 a(n) = sum(2^(A047240(i)-1), i=1..n).

1, 3, 35, 99, 227, 2275, 6371, 14563, 145635, 407779, 932067, 9320675, 26097891, 59652323, 596523235, 1670265059, 3817748707, 38177487075, 106896963811, 244335917283, 2443359172835, 6841405683939, 15637498706147

Offset: 1

Author

Artur Jasinski, Jan 27 2006

Keywords

• nonn
• easy

Examples

			a(2) = 2^(A047240(1)-1) + 2^(A047240(2)-1) = 2^0 + 2^1 = 3
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..300
• Index entries for linear recurrences with constant coefficients, signature (1,0,64,-64).

Crossrefs

Cf. A047240.

Programs

Mathematica

a = {}; s = 0; For[n = 1, n < 48, n++, If[Length[Intersection[{Mod[n, 6]}, {1, 2, 0}]] > 0, s = s + 2^(n - 1); AppendTo[a, s]]]; a
CoefficientList[Series[(1 + 2 x + 32 x^2)/((-1 + x) (-1 + 4 x) (1 + 4 x + 16 x^2)), {x, 0, 25}], x] (* Vincenzo Librandi, May 20 2013 *)
LinearRecurrence[{1,0,64,-64},{1,3,35,99},30] (* Harvey P. Dale, May 11 2025 *)

Formula

G.f.: x*(1+2*x+32*x^2)/((-1+x)*(-1+4*x)*(1+4*x+16*x^2)). - Vaclav Kotesovec, Nov 28 2012

Extensions

Edited by Stefan Steinerberger, Jul 24 2007