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
KEYWORD
easy,nonn,base
AUTHOR
Zerinvary Lajos, Feb 03 2007
STATUS
approved