A112685 a(n)=5a(n-2)+2a(n-3).

1, 1, 1, 7, 7, 37, 49, 199, 319, 1093, 1993, 6103, 12151, 34501, 72961, 196807, 433807, 1129957, 2562649, 6517399, 15073159, 37712293, 88400593, 218707783, 517427551, 1270340101, 3024553321, 7386555607, 17663446807, 42981884677, 103090345249

Offset: 0

Author

Paul Curtz, Mar 02 2008

Keywords

• nonn

Comments

Last digit has period 12.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,5,2).

Programs

Mathematica

nxt[{a_,b_,c_}]:={b,c,5b+2a}; NestList[nxt,{1,1,1},30][[;;,1]] (* or *) LinearRecurrence[{0,5,2},{1,1,1},40] (* Harvey P. Dale, Dec 15 2023 *)

Formula

Differences: 0, 0, 6, 0, 30, 12, 150, 120, 774 ... = 6*A135138.

O.g.f.: (-1-x+4*x^2)/((2*x+1)(x^2+2*x-1)) . a(n) = [(-2)^(n+1)+9*A000129(n+1)-15*A000129(n)]/7. - R. J. Mathar, Mar 17 2008

Extensions

More terms from R. J. Mathar, Mar 17 2008