A075411 Squares of A002276.

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

Offset

0,2

Comments

A transformation of the Wonderful Demlo numbers (A002477).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

G. Villemin, Variations sur les carrés

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

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

Example

a(2) = 22^2 = 484.

Mathematica

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

Prog

(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

Crossrefs

Cf. A075411, A075412, A075413, A075414, A075415, A075416, A075417, A002283.

Sequence in context: A027678 A058442 A221242 * A114763 A069500 A053953

Adjacent sequences: A075408 A075409 A075410 * A075412 A075413 A075414

Keyword

easy,nonn

Author

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

Status

approved