A049868 a(n) = Sum{a(k): k=0,1,2,...,n-4,n-2,n-1}; a(n-3) is not a summand; initial terms are 1,2,2.

1, 2, 2, 4, 7, 14, 26, 49, 91, 170, 317, 592, 1105, 2063, 3851, 7189, 13420, 25052, 46766, 87301, 162970, 304226, 567917, 1060165, 1979074, 3694457, 6896666, 12874423, 24033463, 44864717, 83751677, 156344314, 291857374, 544827788, 1017062939, 1898612818

Offset

0,2

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (2,0,-1,1).

Formula

a(n) = 2*a(n-1) - a(n-3) + a(n-4).

G.f.: (1-2x^2+x^3)/(1-2x+x^3-x^4). - Ralf Stephan, Mar 11 2003

Asymptotic to b*c^n, with b=0.617072414.., c=1.8667604.. - Ralf Stephan, Mar 11 2003

Mathematica

LinearRecurrence[{2, 0, -1, 1}, {1, 2, 2, 4}, 40] (* Harvey P. Dale, Sep 03 2018 *)

Crossrefs

Sequence in context: A109070 A169973 A300353 * A120363 A118988 A049904

Adjacent sequences: A049865 A049866 A049867 * A049869 A049870 A049871

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved