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

Author

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

Keywords

• nonn
• less

Examples

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

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).

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.

Programs

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]] (* or *) LinearRecurrence[{0,20,0,-99},{0,1,1,10},30] (* Harvey P. Dale, May 03 2018 *)

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)). [From R. J. Mathar, Jul 13 2009]

Extensions

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

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