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%I #21 Jun 19 2021 12:35:05
%S 0,1,1,10,20,101,301,1030,4040,10601,51001,110050,620060,1151501,
%T 7352101,12135070,85656080,128702801,985263601,1372684090,11225320100,
%U 14712104501,126965305501,158346365110,1427999420120
%N 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.
%H Harvey P. Dale, <a href="/A161999/b161999.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 20, 0, -99).
%F 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]
%e As pairs:
%e 0, 1
%e 1, 10
%e 20, 101
%e 301, 1030
%e 4040, 10601
%e 51001, 110050
%e 620060, 1151501
%e 7352101, 12135070
%e 85656080, 128702801
%t 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 *)
%Y 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)
%Y Cf. A162849.
%K nonn,less
%O 1,4
%A _Mark Dols_, Jun 24 2009, Jun 28 2009, Jul 13 2009
%E Edited by _N. J. A. Sloane_, Jun 30 2009
%E NAME adapted to offset. - _R. J. Mathar_, Jun 19 2021
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