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

0, 1, 22, 464, 9658, 199666, 4112922, 84558014, 1736623658, 35646098566, 731452470122, 15006822709814, 307859627711658, 6315326642698966, 129547066718721322, 2657377349777550614, 54509922224486463658, 1118139793621467673366, 22935894163202834676522, 470473020119757115115414

Offset: 0

Author

Ilya Gutkovskiy, Sep 08 2016

Keywords

• nonn
• easy

Links

• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Repunit
• Index entries for linear recurrences with constant coefficients, signature (33,-272,330,-100)

Crossrefs

Cf. A000035, A002275, A063524.

Cf. A030267 (self-composition of the natural numbers), A030279 (self-composition of the squares), A030280 (self-composition of the triangular numbers).

Programs

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

Mathematica

LinearRecurrence[{33, -272, 330, -100}, {0, 1, 22, 464}, 20]

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

Formula

O.g.f.: x*(1 - x)*(1 - 10*x)/((1 - 21*x + 10*x^2)*(1 - 12*x + 10*x^2)).

a(n) = 33*a(n-1) - 272*a(n-2) + 330*a(n-3) - 100*a(n-4) for n > 3.

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)).

A000035(a(n)) = A063524(n).