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 A125857 Numbers whose base-9 representation is 22222222.......2. 4
 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 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 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

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Last modified June 15 00:00 EDT 2021. Contains 345041 sequences. (Running on oeis4.)