0,4

Denominator of continued fraction given by C(n) = [ 1; 2,3,4,...n ]. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 02 2001. Cf. A001040.

If initial 1 is omitted, CONTINUANT transform of 0, 1, 2, 3, 4, 5, ...

Number of deco polyominoes of height n having no 1-cell columns. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column. Example: a(2)=1 because the vertical and horizontal dominoes are the deco polynomioes of height 2, of which only the vertical domino does not have 1-cell columns. a(n)=A121554(n,0). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 16 2006

Archimedeans Problems Drive, Eureka, 20 (1957), 15.

E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.

T. D. Noe, Table of n, a(n) for n=0..100

N. J. A. Sloane, Transforms

a(-n)=a(n). - Michael Somos Sep 25 2005

a(5) = 4*a(4) + a(3) = 4*7+2 = 30.

a[0]:=1: a[1]:=0: for n from 2 to 23 do a[n]:=(n-1)*a[n-1]+a[n-2] od: seq(a[n], n=0..23); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 16 2006

a[0] = 1; a[1] = 0; a[n_] := (n - 1)*a[n - 1] + a[n - 2]; Table[ a[n], {n, 0, 21}] (from Robert G. Wilson v Feb 24 2005)

(PARI) a(n)=contfracpnqn(vector(abs(n), i, i))[2, 2] /* Michael Somos Sep 25 2005 */

A column of A058294.

See also the constant in A060997.

Cf. A121554.

Sequence in context: A030975 A066114 A088128 this_sequence A124552 A020045 A020135

Adjacent sequences: A001050 A001051 A001052 this_sequence A001054 A001055 A001056

easy,nonn,nice,frac

njas, R. K. Guy

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 19 2000