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%I #43 Feb 21 2024 08:18:07
%S 0,1,2,12,22,122,222,1222,2222,12222,22222,122222,222222,1222222,
%T 2222222,12222222,22222222,122222222,222222222,1222222222,2222222222,
%U 12222222222,22222222222,122222222222,222222222222,1222222222222,2222222222222,12222222222222
%N Expansion of x*(1+x)/((1-x)*(1-10*x^2)).
%C Previous name: Sequence whose n-th term digits sum to n.
%C a(n) is the smallest integer with digits from {0,1,2} having digit sum n. Namely the base-10 reading of the ternary string of A062318. - _Jason Kimberley_, Nov 01 2011
%C a(n) is the Moore lower bound on the order of an (11,n)-cage. - _Jason Kimberley_, Oct 18 2011
%H Colin Barker, <a href="/A094626/b094626.txt">Table of n, a(n) for n = 0..1000</a>
%H G. Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cages/allcages.html">Cages of higher valency</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,10,-10).
%F G.f.: x*(1+x)/((1-x)*(1-10*x^2)).
%F a(n) = 10^(n/2)*(11*sqrt(10)/180 + 1/9 - (11*sqrt(10)/180 - 1/9)*(-1)^n) - 2/9.
%F From _Colin Barker_, Mar 17 2017: (Start)
%F a(n) = 2*(10^(n/2) - 1)/9 for n even.
%F a(n) = (11*10^((n-1)/2) - 2)/9 for n odd. (End)
%F E.g.f.: (20*(cosh(sqrt(10)*x) - cosh(x) - sinh(x)) + 11*sqrt(10)*sinh(sqrt(10)*x))/90. - _Stefano Spezia_, Apr 09 2022
%t LinearRecurrence[{1, 10, -10}, {0, 1, 2}, 30] (* _Paolo Xausa_, Feb 21 2024 *)
%o (PARI) concat(0, Vec(x*(1+x)/((1-x)*(1-10*x^2)) + O(x^30))) \\ _Colin Barker_, Mar 17 2017
%Y Cf. A094623, A094624.
%Y Moore lower bound on the order of a (k,g) cage: A198300 (square); rows: A000027 (k=2), A027383 (k=3), A062318 (k=4), A061547 (k=5), A198306 (k=6), A198307 (k=7), A198308 (k=8), A198309 (k=9), A198310 (k=10), this sequence (k=11); columns: A020725 (g=3), A005843 (g=4), A002522 (g=5), A051890 (g=6), A188377 (g=7). - _Jason Kimberley_, Nov 01 2011
%K easy,nonn,base
%O 0,3
%A _Paul Barry_, May 15 2004
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