A309907 a(n) is the square of the number consisting of one 1 and n 3's: (133...3)^2.

1, 169, 17689, 1776889, 177768889, 17777688889, 1777776888889, 177777768888889, 17777777688888889, 1777777776888888889, 177777777768888888889, 17777777777688888888889, 1777777777776888888888889, 177777777777768888888888889, 17777777777777688888888888889

Offset: 0

Author

Alois P. Heinz, Aug 21 2019

Keywords

• nonn
• base
• easy

Comments

All terms are zeroless (elements of A052382).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Crossrefs

Cf. A052382, A097166, A102807.

Programs

Maple

a:= n-> parse(cat(1, 3$n))^2:
seq(a(n), n=0..18);

PARI

{a(n) = ((4*10^n-1)/3)^2} \\ Seiichi Manyama, Aug 23 2019

Formula

G.f.: -(40*x^2+58*x+1)/((x-1)*(100*x-1)*(10*x-1)).

a(n) = A097166(n)^2 = ((4*10^n-1)/3)^2. - Seiichi Manyama, Aug 23 2019