A075413 Squares of A002278.

0, 16, 1936, 197136, 19749136, 1975269136, 197530469136, 19753082469136, 1975308602469136, 197530863802469136, 19753086415802469136, 1975308641935802469136, 197530864197135802469136, 19753086419749135802469136, 1975308641975269135802469136, 197530864197530469135802469136

Offset

0,2

Comments

A transformation of the Wonderful Demlo numbers (A002477).

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).

Formula

a(n) = A002278(n)^2 = (4*A002275(n))^2 = 16*A002275(n)^2.

From Colin Barker, Jul 17 2019: (Start)

G.f.: 16*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) = 16*(10^n-1)^2/81. (End)

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

E.g.f.: 16*exp(x)*(1 - 2*exp(9*x) + exp(99*x))/81.

a(n) = 16*A002477(n). (End)

Example

a(2) = 44^2 = 1936.

Mathematica

16*(10^Range[0, 15] - 1)^2/81 (* Paolo Xausa, May 09 2026 *)

Prog

(PARI) concat(0, Vec(16*x*(1 + 10*x) / ((1 - x)*(1 - 10*x)*(1 - 100*x)) + O(x^20))) \\ Colin Barker, Jul 17 2019

Crossrefs

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

Cf. A002275, A002278, A002283, A002477.

Sequence in context: A160306 A393768 A167000 * A265213 A176886 A159389

Adjacent sequences: A075410 A075411 A075412 * A075414 A075415 A075416

Keyword

easy,nonn

Author

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

Status

approved