A079162 a(n) = 5a(n-2) - 2a(n-4).

0, 1, 2, 4, 10, 18, 46, 82, 210, 374, 958, 1706, 4370, 7782, 19934, 35498, 90930, 161926, 414782, 738634, 1892050, 3369318, 8630686, 15369322, 39369330, 70107974, 179585278, 319801226, 819187730, 1458790182, 3736768094

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (0,5,0,-2).

Formula

Also a(n) = a(n-1) + 2a(n-2) if n is odd, else a(n) = 2a(n-1) + a(n-2).

a(2n) = 2*A005824(2n), a(2n+1) = A005824(2n) + A005824(2n+1).

G.f.: x*(1+2*x-x^2)/(1-5*x^2+2*x^4).

a(n)=(1/68) * (-1)^n * [5/2 + (1/2) * sqrt(17)]^(-1/4) * [5/2 + (1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2 + (1/2) * sqrt(17)]^(1/2) * n * sqrt(17)-(1/68) * [5/2-(1/2) * sqrt(17)]^(-1/4) * (-1)^n * sqrt(17) * [5/2 -(1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2-(1/2) * sqrt(17)]^(1/ 2) * n + (1/4) * [5/2-(1/2) * sqrt(17)]^( -1/4) * [5/2-(1/2) * sqrt(17)]^[(1/ 4) * (-1)^n] * [5/2-(1/2) * sqrt(17)]^(1/2) * n + (1/4) * [5/2 + (1/2) * sqrt(17)]^(-1/4) * [5/2 + (1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2 + (1/2) * sqrt(17)]^(1/2) * n-(1/4) * (-1)^n * [5/2 + (1/2) * sqrt(17)]^(-1/4) * [5/2 + (1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2 + (1/2) * sqrt(17)]^[(1/2) * n]-(1/4) * [5/2-(1/2) * sqrt(17)]^(-1/ 4) * (-1)^n * [5/2-(1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2-(1/2) * sqrt(17)]^(1/2) * n + (7/68) * [5/2 + (1/2) * sqrt(17)]^(-1/4) * [5/2 + (1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2 + (1/2) * sqrt(17)]^(1/ 2) * n * sqrt(17)-(7/68) * [5/2-(1/2) * sqrt(17)]^(-1/4) * sqrt(17) * [5/2-(1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2-(1/2) * sqrt(17)]^[(1 /2) * n], with n>=0 [From Paolo P. Lava, Oct 06 2008]

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = If[ OddQ[n], a[n - 1] + 2a[n - 2], 2a[n - 1] + a[n - 2]]; Table[a[n], {n, 0, 30}]
LinearRecurrence[{0, 5, 0, -2}, {0, 1, 2, 4}, 40] (* Harvey P. Dale, Jul 05 2022 *)

Crossrefs

Cf. A005824. a(2n+1) = A052913(n).

Sequence in context: A348396 A104723 A206140 * A257593 A197926 A228705

Adjacent sequences: A079159 A079160 A079161 * A079163 A079164 A079165

Keyword

nonn

Author

Robert G. Wilson v, Dec 29 2002

Extensions

Corrected the g.f. and index in formula with A052913 R. J. Mathar, Apr 01 2009, May 02 2009

Status

approved