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A276644 Self-composition of the repunits; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A002275.

%I A276644 #15 Feb 16 2025 08:33:36
%S A276644 0,1,22,464,9658,199666,4112922,84558014,1736623658,35646098566,
%T A276644 731452470122,15006822709814,307859627711658,6315326642698966,
%U A276644 129547066718721322,2657377349777550614,54509922224486463658,1118139793621467673366,22935894163202834676522,470473020119757115115414
%N A276644 Self-composition of the repunits; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A002275.
%H A276644 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A276644 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repunit.html">Repunit</a>
%H A276644 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (33,-272,330,-100)
%F A276644 O.g.f.: x*(1 - x)*(1 - 10*x)/((1 - 21*x + 10*x^2)*(1 - 12*x + 10*x^2)).
%F A276644 a(n) = 33*a(n-1) - 272*a(n-2) + 330*a(n-3) - 100*a(n-4) for n > 3.
%F A276644 a(n) = ((6 - sqrt(26))^n - (6 + sqrt(26))^n)/(18*sqrt(26)) + 10*(((21 + sqrt(401))/2)^n - ((21 - sqrt(401))/2)^n)/(9*sqrt(401)).
%F A276644 A000035(a(n)) = A063524(n).
%t A276644 LinearRecurrence[{33, -272, 330, -100}, {0, 1, 22, 464}, 20]
%o A276644 (PARI) concat(0, Vec(x*(1-x)*(1-10*x)/((1-21*x+10*x^2)*(1-12*x+10*x^2)) + O(x^99))) \\ _Altug Alkan_, Sep 08 2016
%o A276644 (Magma) I:=[0,1,22,464]; [n le 4 select I[n] else 33*Self(n-1)-272*Self(n-2)+330*Self(n-3)-100*Self(n-4): n in [1..20]]; // _Vincenzo Librandi_, Sep 09 2016
%Y A276644 Cf. A000035, A002275, A063524.
%Y A276644 Cf. A030267 (self-composition of the natural numbers), A030279 (self-composition of the squares), A030280 (self-composition of the triangular numbers).
%K A276644 nonn,easy
%O A276644 0,3
%A A276644 _Ilya Gutkovskiy_, Sep 08 2016