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%I #24 Jan 02 2024 08:57:14
%S 1,4,7,10,40,70,100,400,700,1000,4000,7000,10000,40000,70000,100000,
%T 400000,700000,1000000,4000000,7000000,10000000,40000000,70000000,
%U 100000000,400000000,700000000,1000000000,4000000000,7000000000
%N a(3n)=10^n. a(3n+1)=4*10^n. a(3n+2)=7*10^n.
%H G. C. Greubel, <a href="/A135262/b135262.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,10).
%F From _R. J. Mathar_, Jul 22 2008: (Start)
%F a(n) = 10*a(n-3).
%F O.g.f.: (1+4*x+7*x^2)/(1-10*x^3). (End)
%p seq(coeff(series((1+4*x+7*x^2)/(1-10*x^3), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Nov 21 2019
%t Flatten[Table[FromDigits[PadRight[{i},n,0]],{n,10},{i,{1,4,7}}]] (* or *) LinearRecurrence[{0,0,10},{1,4,7},30] (* _Harvey P. Dale_, Jun 06 2015 *)
%o (PARI) my(x='x+O('x^30)); Vec((1+4*x+7*x^2)/(1-10*x^3)) \\ _G. C. Greubel_, Nov 21 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+4*x+7*x^2)/(1-10*x^3) )); // _G. C. Greubel_, Nov 21 2019
%o (Sage)
%o def A135262_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P((1+4*x+7*x^2)/(1-10*x^3)).list()
%o A135262_list(30) # _G. C. Greubel_, Nov 21 2019
%o (GAP) a:=[1,4,7];; for n in [4..30] do a[n]:=10*a[n-3]; od; a; # _G. C. Greubel_, Nov 21 2019
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Dec 01 2007
%E Name edited by _R. J. Mathar_, Jul 22 2008
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