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%I #20 Feb 22 2024 09:02:30
%S 0,1,11,12,121,122,1221,1222,12221,12222,122221,122222,1222221,
%T 1222222,12222221,12222222,122222221,122222222,1222222221,1222222222,
%U 12222222221,12222222222,122222222221,122222222222,1222222222221,1222222222222,12222222222221
%N Expansion of g.f. x*(1+11*x+x^2)/((1-x)*(1+x)*(1-10*x^2)).
%C Previous name: "Sequence whose n-th term digits sum to n."
%C n-th term digits are reversals of A094623(n).
%H Colin Barker, <a href="/A094624/b094624.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,11,0,-10).
%F a(n) = 10^(n/2)*(11/18 + 11*sqrt(10)/180 - (11*sqrt(10)/180 - 11/18)(-1)^n) - 13/18 - (-1)^n/2.
%F From _Colin Barker_, Dec 01 2015: (Start)
%F a(n) = 11*a(n-2) - 10*a(n-4) for n > 3.
%F G.f.: x*(1+11*x+x^2) / ((1-x)*(1+x)*(1-10*x^2)). (End)
%F E.g.f.: (110*(cosh(sqrt(10)*x) - cosh(x)) + 11*sqrt(10)*sinh(sqrt(10)*x) - 20*sinh(x))/90. - _Stefano Spezia_, Feb 21 2024
%t LinearRecurrence[{0, 11, 0, -10}, {0, 1, 11, 12}, 30] (* _Paolo Xausa_, Feb 22 2024 *)
%o (PARI) concat(0, Vec(x*(1+11*x+x^2)/((1-x)*(1+x)*(1-10*x^2)) + O(x^40))) \\ _Colin Barker_, Dec 01 2015
%Y Cf. A094623, A094625, A094626.
%K nonn,base,easy
%O 0,3
%A _Paul Barry_, May 15 2004
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