A075417 Squares of A002282: a(n) = (8*(10^n - 1)/9)^2.

0, 64, 7744, 788544, 78996544, 7901076544, 790121876544, 79012329876544, 7901234409876544, 790123455209876544, 79012345663209876544, 7901234567743209876544, 790123456788543209876544, 79012345678996543209876544, 7901234567901076543209876544, 790123456790121876543209876544

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) = 88^2 = 7744.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..100
• 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, A002282, A002283, A002477.

Programs

PARI

concat(0, Vec(64*x*(1 + 10*x) / ((1 - x)*(1 - 10*x)*(1 - 100*x)) + O(x^20))) \\ Colin Barker, Jul 17 2019

Formula

a(n) = A002282(n)^2 = (8*A002275(n))^2 = 64*A002275(n)^2.

From Colin Barker, Jul 17 2019: (Start)

G.f.: 64*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)).

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

a(n) = 64*(10^n-1)^2/81. (End)

From Elmo R. Oliveira, Jul 30 2025: (Start)

E.g.f.: 64*exp(x)*(1 - 2*exp(9*x) + exp(99*x))/81.

a(n) = 64*A002477(n). (End)