# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a125857 Showing 1-1 of 1 %I A125857 #66 Nov 05 2020 05:04:39 %S A125857 0,2,20,182,1640,14762,132860,1195742,10761680,96855122,871696100, %T A125857 7845264902,70607384120,635466457082,5719198113740,51472783023662, %U A125857 463255047212960,4169295424916642,37523658824249780,337712929418248022 %N A125857 Numbers whose base-9 representation is 22222222.......2. %C A125857 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 %H A125857 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 %H A125857 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 %H A125857 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. %H A125857 R. J. Mathar, Counting Walks on Finite Graphs, Nov 2020, Section 5. %H A125857 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. %H A125857 Index entries for linear recurrences with constant coefficients, signature (10,-9). %F A125857 a(n) = (9^(n-1) - 1)*2/8. %F A125857 a(n) = 9*a(n-1) + 2 (with a(1)=0). - _Vincenzo Librandi_, Sep 30 2010 %F A125857 a(n) = 2 * A002452(n). - _Vladimir Pletser_, Mar 29 2014 %F A125857 From _Colin Barker_, Sep 30 2014: (Start) %F A125857 a(n) = 10*a(n-1) - 9*a(n-2). %F A125857 G.f.: 2*x^2 / ((x-1)*(9*x-1)). (End) %F A125857 a(n) = -a(2-n) * 9^(n-1) for all n in Z. - _Michael Somos_, Jul 02 2017 %F A125857 a(n) = A191681(n-1)/2. - _Klaus Purath_, Jul 03 2020 %e A125857 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 %p A125857 seq((9^n-1)*2/8, n=0..19); %t A125857 FromDigits[#, 9]&/@Table[PadRight[{2}, n, 2], {n, 0, 20}] (* _Harvey P. Dale_, Feb 02 2011 *) %t A125857 Table[(9^(n - 1) - 1)*2/8, {n, 20}] (* _Wesley Ivan Hurt_, Mar 29 2014 *) %o A125857 (PARI) Vec(2*x^2/((x-1)*(9*x-1)) + O(x^100)) \\ _Colin Barker_, Sep 30 2014 %o A125857 (PARI) {a(n) = (9^(n-1) - 1)/4}; /* _Michael Somos_, Jul 02 2017 */ %Y A125857 Cf. A002452. %K A125857 easy,nonn,base %O A125857 1,2 %A A125857 _Zerinvary Lajos_, Feb 03 2007 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE