A079162 a(n) = 5*a(n-2) - 2*a(n-4), with initial terms 0,1,2,4.

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, 6654348458, 17045465010, 30354161926, 77753788862

Offset: 0

Author

Robert G. Wilson v, Dec 29 2002

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Sean A. Irvine, Walks on Graphs.
• Index entries for linear recurrences with constant coefficients, signature (0,5,0,-2).

Crossrefs

Cf. A005824, A052913.

Programs

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 *)

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

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

Extensions

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

a(31) onwards from Andrew Howroyd, Mar 19 2025