A161999 For n even a(n) = a(n-1) + 10*a(n-2), for n odd a(n) = a(n-3) + 10 a(n-2); with a(1) = 0, a(2) = 1.

0, 1, 1, 10, 20, 101, 301, 1030, 4040, 10601, 51001, 110050, 620060, 1151501, 7352101, 12135070, 85656080, 128702801, 985263601, 1372684090, 11225320100, 14712104501, 126965305501, 158346365110, 1427999420120

Offset

1,4

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0, 20, 0, -99).

Formula

a(n)=20*a(n-2)-99*a(n-4). G.f.: -x^2*(-1-x+10*x^2)/((3*x-1)*(3*x+1)*(11*x^2-1)). - R. J. Mathar, Jul 13 2009

Example

As pairs:
0, 1
1, 10
20, 101
301, 1030
4040, 10601
51001, 110050
620060, 1151501
7352101, 12135070
85656080, 128702801

Mathematica

nxt[{n_, a_, b_, c_}]:={n+1, b, c, If[OddQ[n], c+10b, a+10b]}; NestList[nxt, {2, 0, 1, 1}, 30][[All, 2]] (* Harvey P. Dale, May 03 2018 *)
(* Alternative: *)
LinearRecurrence[{0, 20, 0, -99}, {0, 1, 1, 10}, 30] (* Harvey P. Dale, May 03 2018 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -99, 0, 20, 0]^(n-1)*[0; 1; 1; 10])[1, 1] \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Combination of A081192 and A016190. Triangle A007318 (even /uneven rows). Partly same function as A015446. A001020 (as sum of pairs of 2n).A001019 (as difference of pairs of 2n)

Cf. A162849.

Sequence in context: A166641 A101244 A260743 * A086069 A220012 A154330

Adjacent sequences: A161996 A161997 A161998 * A162000 A162001 A162002

Keyword

nonn,less,easy

Author

Mark Dols, Jun 24 2009, Jun 28 2009, Jul 13 2009

Extensions

Edited by N. J. A. Sloane, Jun 30 2009

NAME adapted to offset. - R. J. Mathar, Jun 19 2021

Status

approved