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
Examples
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
Links
- 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).
Crossrefs
Cf. A002452.
Programs
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Maple
seq((9^n-1)*2/8, n=0..19);
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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 *) -
PARI
Vec(2*x^2/((x-1)*(9*x-1)) + O(x^100)) \\ Colin Barker, Sep 30 2014
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PARI
{a(n) = (9^(n-1) - 1)/4}; /* Michael Somos, Jul 02 2017 */
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
Comments