0,2

All members of sequence are also hex, or central hexagonal, numbers (A003215). (If n is a hex number, 9n - 2 is always a hex number; see recurrence.) - Matthew Vandermast (ghodges14(AT)comcast.net), Mar 30 2003

The sequence 1,1,7,61,547,... with g.f. (1-9x+6x^2)/((1-x)(1-9x)), and a(n) =A054879(n)/3+2*0^n/3 gives the denominators in the probability that a random walk on the cube returns to its starting corner on the 2n-th step. - Paul Barry (pbarry(AT)wit.ie), Mar 11 2004

M. Kac. Random walk and the theory of Brownian motion. Amer. Math. Monthly, 54:369-391, 1947

Eric Weisstein's World of Mathematics, Repunit

a(n) = (3^(2*n+1)+1)/4. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 22 2002

a(n)= 9 {a(n-1)}-2. - Matthew Vandermast (ghodges14(AT)comcast.net), Mar 30 2003

G.f.: (1-3x)/((1-x)(1-9x)). E.g.f. (3exp(9x)+exp(x))/4 - Paul Barry (pbarry(AT)wit.ie), Apr 21 2003

Let _x denote the sequence offset. Then a(n+1)_0 = A083884(n+1)_0 + 2A002452(n+1)_1; (a(n)) = posseq(.5'kk' + 2'ij' - 2'ji' + 4.5e) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Nov 19 2004

a(n) = (-1)^n times the (i, i)-th element of M^n (for any i), where M = ((1, 1, 1, -2), (1, 1, -2, 1), (1, -2, 1, 1), (-2, 1, 1, 1)). - Simone Severini (ss54(AT)york.ac.uk), Nov 25 2004

a(n)=sum{k=0..n, binomial(2n+1, 2k)4^(n-k)} - Paul Barry (pbarry(AT)wit.ie), Jan 22 2005

seq((3^(2*n+1) + 1)/4, n=0..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2007

A054880(n) + 1.

Sequence in context: A135165 A104093 A015572 this_sequence A108448 A098659 A113718

Adjacent sequences: A066440 A066441 A066442 this_sequence A066444 A066445 A066446

nonn

John W. Layman (layman(AT)math.vt.edu), Aug 12 2002

Corrected by Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 22 2002