A178634 a(n) = 63 * ((10^n - 1)/9)^2.

63, 7623, 776223, 77762223, 7777622223, 777776222223, 77777762222223, 7777777622222223, 777777776222222223, 77777777762222222223, 7777777777622222222223, 777777777776222222222223, 77777777777762222222222223, 7777777777777622222222222223, 777777777777776222222222222223

Offset

1,1

References

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See Table 33 at p. 62.

Walther Lietzmann, Lustiges und Merkwuerdiges von Zahlen und Formen, (F. Hirt, Breslau 1921-43), p. 149.

Links

G. C. Greubel, Table of n, a(n) for n = 1..200

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

Formula

a(n) = 63*A002477(n) = A002283(n)*A002281(n).

a(n) = ((A002281(n-1)*10 + 6)*10^(n-1) + A002276(n-1))*10 + 3.

G.f.: 63*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - Ilya Gutkovskiy, Feb 24 2017

E.g.f.: 7*exp(x)*(1 - 2*exp(9*x) + exp(99*x))/9. - Stefano Spezia, Jul 31 2024

Example

n=1: ..................... 63 = 9 * 7;
n=2: ................... 7623 = 99 * 77;
n=3: ................. 776223 = 999 * 777;
n=4: ............... 77762223 = 9999 * 7777;
n=5: ............. 7777622223 = 99999 * 77777;
n=6: ........... 777776222223 = 999999 * 777777;
n=7: ......... 77777762222223 = 9999999 * 7777777;
n=8: ....... 7777777622222223 = 99999999 * 77777777;
n=9: ..... 777777776222222223 = 999999999 * 777777777.

Mathematica

63((10^Range[15]-1)/9)^2 (* or *) Table[FromDigits[Join[PadRight[{}, n, 7], {6}, PadRight[{}, n, 2], {3}]], {n, 0, 15}] (* Harvey P. Dale, Apr 23 2012 *)

Prog

(Magma) [63*((10^n - 1)/9)^2: n in [1..20]]; // Vincenzo Librandi, Dec 28 2010
(PARI) a(n)=63*(10^n\9)^2 \\ Charles R Greathouse IV, Jul 02 2013
(Sage) [63*((10^n - 1)/9)^2 for n in (1..20)] # G. C. Greubel, Jan 28 2019
(GAP) List([1..20], n -> 63*((10^n - 1)/9)^2); # G. C. Greubel, Jan 28 2019

Crossrefs

Cf. A075412, A178630, A178631, A075415, A178632, A178633, A178635, A059988.

Cf. A002276, A002281, A002283, A002477.

Sequence in context: A234616 A093263 A069433 * A174763 A160871 A183525

Adjacent sequences: A178631 A178632 A178633 * A178635 A178636 A178637

Keyword

nonn,easy

Author

Reinhard Zumkeller, May 31 2010

Status

approved