A141025 a(n) = (2^(2+n)-(-1)^n)/3 - 2*n.

1, 1, 1, 5, 13, 33, 73, 157, 325, 665, 1345, 2709, 5437, 10897, 21817, 43661, 87349, 174729, 349489, 699013, 1398061, 2796161, 5592361, 11184765, 22369573, 44739193, 89478433, 178956917, 357913885, 715827825, 1431655705, 2863311469, 5726622997, 11453246057, 22906492177

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

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

a(n) = A001045(n+2) - 2*n.

a(n+1) - a(n) = 4*A000975(n-1).

a(n+1) - 2*a(n)= 2*(n-1) + (-1)^n = -1, -1, 3, 3, 7, 7, 11, 11,... duplicated A004767.

G.f. ( -1+2*x+x^2-6*x^3 ) / ( (1+x)*(2*x-1)*(x-1)^2 ). - R. J. Mathar, Jul 07 2011

Mathematica

CoefficientList[Series[(-1 + 2*x + x^2 - 6*x^3)/((1 + x)*(2*x - 1)*(x - 1)^2), {x, 0, 50}], x] (* G. C. Greubel, Oct 11 2017 *)

Prog

(Magma) [(2^(2+n)-(-1)^n)/3-2*n: n in [0..40]]; // Vincenzo Librandi, Aug 08 2011
(PARI) for(n=0, 50, print1((2^(2+n)-(-1)^n)/3 - 2*n, ", ")) \\ G. C. Greubel, Oct 11 2017

Crossrefs

Sequence in context: A308812 A321124 A001981 * A100227 A185454 A278764

Adjacent sequences: A141022 A141023 A141024 * A141026 A141027 A141028

Keyword

nonn,easy

Author

Paul Curtz, Jul 29 2008

Extensions

Definition replaced by closed form by R. J. Mathar, Jul 07 2011

Status

approved