A309827 a(n) is the square of the number consisting of one 1 and n 6's: (166...6)^2.

1, 256, 27556, 2775556, 277755556, 27777555556, 2777775555556, 277777755555556, 27777777555555556, 2777777775555555556, 277777777755555555556, 27777777777555555555556, 2777777777775555555555556, 277777777777755555555555556, 27777777777777555555555555556

Offset

0,2

Comments

All terms are zeroless (element 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

a(n) = A246057(n)^2 = ((5*10^n-2)/3)^2.

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

G.f.: (1+145*x+250*x^2)/((1-x)*(1-10*x)*(1-100*x)).

Mathematica

LinearRecurrence[{111, -1110, 1000}, {1, 256, 27556}, 20] (* Harvey P. Dale, Dec 13 2021 *)

Prog

(PARI) {a(n) = ((5*10^n-2)/3)^2}
(PARI) N=20; x='x+O('x^N); Vec((1+145*x+250*x^2)/((1-x)*(1-10*x)*(1-100*x)))

Crossrefs

((k*10^n+3-k)/3)^2: A102807 (k=1), A109344 (k=2), A098608 (k=3), A309907 (k=4), this sequence (k=5).

Cf. A052382, A246057.

Sequence in context: A206055 A237134 A205948 * A205019 A017212 A181243

Adjacent sequences: A309824 A309825 A309826 * A309828 A309829 A309830

Keyword

nonn,base

Author

Seiichi Manyama, Aug 23 2019

Status

approved