A309827 - OEIS

%I #37 Dec 13 2021 14:31:37

%S 1,256,27556,2775556,277755556,27777555556,2777775555556,

%T 277777755555556,27777777555555556,2777777775555555556,

%U 277777777755555555556,27777777777555555555556,2777777777775555555555556,277777777777755555555555556,27777777777777555555555555556

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

%C All terms are zeroless (element of A052382).

%H Seiichi Manyama, <a href="/A309827/b309827.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).

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

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

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

%t LinearRecurrence[{111,-1110,1000},{1,256,27556},20] (* _Harvey P. Dale_, Dec 13 2021 *)

%o (PARI) {a(n) = ((5*10^n-2)/3)^2}

%o (PARI) N=20; x='x+O('x^N); Vec((1+145*x+250*x^2)/((1-x)*(1-10*x)*(1-100*x)))

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

%Y Cf. A052382, A246057.

%K nonn,base

%O 0,2

%A _Seiichi Manyama_, Aug 23 2019