A075414 Squares of A002279: a(n) = (5*(10^n - 1)/9)^2.

0, 25, 3025, 308025, 30858025, 3086358025, 308641358025, 30864191358025, 3086419691358025, 308641974691358025, 30864197524691358025, 3086419753024691358025, 308641975308024691358025, 30864197530858024691358025, 3086419753086358024691358025, 308641975308641358024691358025

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) = 55^2 = 3025.
		

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, A002279, A002283, A002477.

Programs

PARI

concat(0, Vec(25*x*(1 + 10*x) / ((1 - x)*(1 - 10*x)*(1 - 100*x)) + O(x^20))) \\ Colin Barker, Jul 17 2019

Formula

a(n) = A002279(n)^2 = (5*A002275(n))^2 = 25*A002275(n)^2.

From Colin Barker, Jul 17 2019: (Start)

G.f.: 25*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) = 25*(10^n-1)^2/81. (End)

From Elmo R. Oliveira, Jul 29 2025: (Start)

E.g.f.: 25*exp(x)*(1 - 2*exp(9*x) + exp(99*x))/81.

a(n) = 25*A002477(n). (End)