A075415 Squares of A002280 or numbers (666...6)^2.

0, 36, 4356, 443556, 44435556, 4444355556, 444443555556, 44444435555556, 4444444355555556, 444444443555555556, 44444444435555555556, 4444444444355555555556, 444444444443555555555556, 44444444444435555555555556, 4444444444444355555555555556, 444444444444443555555555555556

Offset

0,2

Comments

A transformation of the Wonderful Demlo numbers (A002477).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..500

Gérard Villemin, Variations sur les carrés.

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

Formula

a(n) = A002280(n)^2 = (6*A002275(n))^2 = 36*A002275(n)^2.

a(n) = (6*(10^n-1)/9)^2 = (4/9)*(10^(2*n) - 2*10^n + 1), which is n-1 4's, followed by a 3, n-1 5's and a 6. - Ignacio Larrosa Cañestro, Feb 26 2005

From Reinhard Zumkeller, May 31 2010: (Start)

a(n) = ((A002278(n-1)*10 + 3)*10^(n-1) + A002279(n-1))*10 + 6 for n>0.

a(n) = A002283(n)*A002278(n). (End)

G.f.: 36*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - Arkadiusz Wesolowski, Dec 26 2011

From Elmo R. Oliveira, Jul 27 2025: (Start)

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

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

a(n) = 36*A002477(n). (End)

Example

a(2) = 66^2 = 4356.
From Reinhard Zumkeller, May 31 2010: (Start)
n=1: ..................... 36 = 9 * 4;
n=2: ................... 4356 = 99 * 44;
n=3: ................. 443556 = 999 * 444;
n=4: ............... 44435556 = 9999 * 4444;
n=5: ............. 4444355556 = 99999 * 44444;
n=6: ........... 444443555556 = 999999 * 444444;
n=7: ......... 44444435555556 = 9999999 * 4444444;
n=8: ....... 4444444355555556 = 99999999 * 44444444;
n=9: ..... 444444443555555556 = 999999999 * 444444444. (End)

Mathematica

Table[FromDigits[PadRight[{}, n, 6]]^2, {n, 0, 20}] (* Harvey P. Dale, May 20 2021 *)
(* Alternative: *)
LinearRecurrence[ {111, -1110, 1000}, {0, 36, 4356}, 20] (* Harvey P. Dale, May 20 2021 *)

Crossrefs

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

Cf. A059988, A178630, A178631, A178632, A178633, A178634, A178635. [From Reinhard Zumkeller, May 31 2010]

Cf. A002275, A002278, A002279, A002280, A002283, A002477, A052041, A102807, A309827.

Sequence in context: A184270 A187405 A102794 * A127856 A127860 A189148

Adjacent sequences: A075412 A075413 A075414 * A075416 A075417 A075418

Keyword

nonn,easy,changed

Author

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

Extensions

Edited by Alois P. Heinz, Aug 21 2019 (merged with A102794, submitted by Richard C. Schroeppel, Feb 26 2005)

Status

approved