A133993 a(n) = a(n-1) + 3*a(n-2) - a(n-3) - 2*a(n-4), n > 3.

1, 2, 3, 4, 9, 14, 31, 56, 117, 226, 459, 908, 1825, 3638, 7287, 14560, 29133, 58250, 116515, 233012, 466041, 932062, 1864143, 3728264, 7456549, 14913074, 29826171, 59652316, 119304657, 238609286, 477218599, 954437168, 1908874365, 3817748698, 7635497427

Offset

0,2

Links

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (1,3,-1,-2).

Formula

a(n) = 1+4*2^n/9+(-1)^n*(n/3-4/9).

G.f.: ( 1+x-2*x^2-4*x^3 ) / ( (2*x-1)*(x-1)*(1+x)^2 ).

a(n) = 3*a(n-2) + 2*a(n-3) - 4, for n>2. - Greg Dresden, Feb 21 2020

E.g.f.: (1/9)*(4*cosh(2*x) + (13 + 3*x)*sinh(x) + cosh(x)*(5 - 3*x + 8*sinh(x))). - Stefano Spezia, Feb 22 2020

Mathematica

LinearRecurrence[{1, 3, -1, -2}, {1, 2, 3, 4}, 40] (* Harvey P. Dale, Aug 03 2018 *)

Crossrefs

Equals 1 + A103196(n-1) for n>0. - Greg Dresden, Feb 21 2020

Sequence in context: A217787 A077906 A342532 * A341824 A122974 A032982

Adjacent sequences: A133990 A133991 A133992 * A133994 A133995 A133996

Keyword

nonn,easy

Author

Paul Curtz, Jan 22 2008

Extensions

More terms from Harvey P. Dale, Aug 03 2018

Status

approved