

A125857


Numbers whose base9 representation is 22222222.......2.


3



0, 2, 20, 182, 1640, 14762, 132860, 1195742, 10761680, 96855122, 871696100, 7845264902, 70607384120, 635466457082, 5719198113740, 51472783023662, 463255047212960, 4169295424916642, 37523658824249780, 337712929418248022
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

Table of n, a(n) for n=1..20.
G. Benkart, D. Moon, A SchurWeyl Duality Approach to Walking on Cubes, arXiv preprint arXiv:1409.8154 [math.RT], 2014 and Ann. Combin. 20 (3) (2016) 397417
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, 7884
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^(n1)  1)*2/8.
a(n) = 9*a(n1) + 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(n1)  9*a(n2).
G.f.: 2*x^2 / ((x1)*(9*x1)). (End)
a(n) =  9^(n1) * a(2n) for all n in Z.  Michael Somos, Jul 02 2017


MAPLE

seq((9^n1)*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/((x1)*(9*x1)) + O(x^100)) \\ Colin Barker, Sep 30 2014
(PARI) {a(n) = (9^n1)  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



