A075411 Squares of A002276.

0, 4, 484, 49284, 4937284, 493817284, 49382617284, 4938270617284, 493827150617284, 49382715950617284, 4938271603950617284, 493827160483950617284, 49382716049283950617284, 4938271604937283950617284, 493827160493817283950617284, 49382716049382617283950617284

Offset: 0

Author

Michael Taylor (michael.taylor(AT)vf.vodafone.co.uk), Sep 14 2002

Keywords

• easy
• nonn

Comments

A transformation of the Wonderful Demlo numbers (A002477).

Examples

			a(2) = 22^2 = 484.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Gérard Villemin, Variations sur les carrés.
• Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Crossrefs

Cf. A075411, A075412, A075413, A075414, A075415, A075416, A075417.

Cf. A002275, A002276, A002283, A002477.

Programs

Magma

I:=[0,4,484]; [n le 3 select I[n] else 111*Self(n-1)-1110*Self(n-2)+1000*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Apr 25 2017

Mathematica

LinearRecurrence[{111, -1110, 1000}, {0, 4, 484}, 30] (* Vincenzo Librandi, Apr 25 2017 *)

Formula

a(n) = A002276(n)^2 = (2*A002275(n))^2 = 4*A002275(n)^2.

From Chai Wah Wu, Apr 24 2017: (Start)

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

G.f.: 4*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). (End)

a(n) = 4*(10^n - 1)^2/81. - Colin Barker, Apr 25 2017

From Elmo R. Oliveira, Jul 28 2025: (Start)

E.g.f.: 4*exp(x)*(1 - 2*exp(9*x) + exp(99*x))/81.

a(n) = 4*A002477(n). (End)