A125857 Numbers whose base-9 representation is 22222222.......2.

0, 2, 20, 182, 1640, 14762, 132860, 1195742, 10761680, 96855122, 871696100, 7845264902, 70607384120, 635466457082, 5719198113740, 51472783023662, 463255047212960, 4169295424916642, 37523658824249780, 337712929418248022

Offset

1,2

Comments

If f(1) := 1/x and f(n+1) = (f(n) + 2/f(n))/3, then f(n) = 3^(1-n) * (1/x + a(n)*x + O(x^3)). - Michael Somos, Jul 28 2020

Links

Table of n, a(n) for n=1..20.

G. Benkart, D. Moon, A Schur-Weyl Duality Approach to Walking on Cubes, arXiv preprint arXiv:1409.8154 [math.RT], 2014 and Ann. Combin. 20 (3) (2016) 397-417

E. Estrada and J. A. de la Pena, From Integer Sequences to Block Designs via Counting Walks in Graphs, arXiv preprint arXiv:1302.1176 [math.CO], 2013. - From N. J. A. Sloane, Feb 28 2013

E. Estrada and J. A. de la Pena, Integer sequences from walks in graphs, Notes on Number Theory and Discrete Mathematics, Vol. 19, 2013, No. 3, 78-84.

R. J. Mathar, Counting Walks on Finite Graphs, Nov 2020, Section 5.

Vladimir Pletser, Congruence conditions on the number of terms in sums of consecutive squared integers equal to squared integers, arXiv:1409.7969 [math.NT], 2014.

Index entries for linear recurrences with constant coefficients, signature (10,-9).

Formula

a(n) = (9^(n-1) - 1)*2/8.

a(n) = 9*a(n-1) + 2 (with a(1)=0). - Vincenzo Librandi, Sep 30 2010

a(n) = 2 * A002452(n). - Vladimir Pletser, Mar 29 2014

From Colin Barker, Sep 30 2014: (Start)

a(n) = 10*a(n-1) - 9*a(n-2).

G.f.: 2*x^2 / ((x-1)*(9*x-1)). (End)

a(n) = -a(2-n) * 9^(n-1) for all n in Z. - Michael Somos, Jul 02 2017

a(n) = A191681(n-1)/2. - Klaus Purath, Jul 03 2020

Example

G.f. = 2*x^2 + 20*x^3 + 182*x^4 + 1640*x^5 + 14762*x^6 + 132860*x^7 + ... - Michael Somos, Jul 28 2020

Maple

seq((9^n-1)*2/8, n=0..19);

Mathematica

FromDigits[#, 9]&/@Table[PadRight[{2}, n, 2], {n, 0, 20}] (* Harvey P. Dale, Feb 02 2011 *)
Table[(9^(n - 1) - 1)*2/8, {n, 20}] (* Wesley Ivan Hurt, Mar 29 2014 *)

Prog

(PARI) Vec(2*x^2/((x-1)*(9*x-1)) + O(x^100)) \\ Colin Barker, Sep 30 2014
(PARI) {a(n) = (9^(n-1) - 1)/4}; /* Michael Somos, Jul 02 2017 */

Crossrefs

Cf. A002452.

Sequence in context: A067641 A279462 A037566 * A226312 A171076 A287999

Adjacent sequences: A125854 A125855 A125856 * A125858 A125859 A125860

Keyword

easy,nonn,base

Author

Zerinvary Lajos, Feb 03 2007

Status

approved