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

0,2

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).

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

From Elmo R. Oliveira, Dec 03 2025: (Start)

a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3).

E.g.f.: exp(x)*(1 - 8*exp(9*x) + 16*exp(99*x))/9. (End)

Maple

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

Mathematica

LinearRecurrence[{111, -1110, 1000}, {1, 169, 17689}, 20] (* Paolo Xausa, Dec 10 2025 *)

Prog

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

Crossrefs

Cf. A052382, A097166, A102807.

Sequence in context: A264276 A231769 A069297 * A264222 A051477 A227692

Adjacent sequences: A309904 A309905 A309906 * A309908 A309909 A309910

Keyword

nonn,base,easy

Author

Alois P. Heinz, Aug 21 2019

Status

approved