login
This site is supported by donations to The OEIS Foundation.

 

Logo

The October issue of the Notices of the Amer. Math. Soc. has an article about the OEIS.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A055244 Number of certain stackings of n+1 squares on a double staircase. 8
1, 1, 3, 6, 12, 23, 43, 79, 143, 256, 454, 799, 1397, 2429, 4203, 7242, 12432, 21271, 36287, 61739, 104791, 177476, 299978, 506111, 852457, 1433593, 2407443, 4037454, 6762708, 11314391, 18909139, 31569799, 52657247, 87751624 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n)= G_{n+1} of Turban reference eq.(3.9).

Equals A046854 * [1,2,3,...]. [Gary W. Adamson, Dec 23 2008]

(1 + x + 3x^2 + 6x^3 + ...) = (1 + x + 2x^2 + 3x^3 + 5x^4 + 8x^5 + ...) * (1 + x^2 + 2x^3 + 3x^4 + 5x^5 + 8x^6 + ...). [Gary W. Adamson, Jul 27 2010]

Column 1 of A194540 [R. H. Hardin, Aug 28 2011]

REFERENCES

L. Turban, Lattice animals on a staircase and Fibonacci numbers, J.Phys. A 33 (2000) 2587-2595.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: (1-x+x^3)/(1-x-x^2)^2 (from Turban reference eq.(3.3) with t=1).

a(n)=((n+5)*F(n+1)+(2*n-3)*F(n))/5 with F(n)=A000045(n) (Fibonacci numbers) (from Turban reference eq.(3.9)).

a(n) = A001629(n+1) + F(n-1). - Gary W. Adamson, Jul 27 2007

a(n) = (((n-4)*n-6)*a(n-2) + ((n-5)*n-11)*a(n-1)) / ((n-6)*n-1). - Jean-François Alcover, Mar 11 2014

MAPLE

a:= n-> (Matrix([[1, -1, 2, -4]]). Matrix(4, (i, j)-> if (i=j-1) then 1 elif j=1 then [2, 1, -2, -1][i] else 0 fi)^(n))[1, 1] ; seq (a(n), n=0..33); # Alois P. Heinz, Aug 05 2008

MATHEMATICA

a[0] = a[1] = 1; a[n_] := a[n] = (((n-4)*n-6)*a[n-2] + ((n-5)*n-11)*a[n-1]) / ((n-6)*n-1); Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Mar 11 2014 *)

CoefficientList[Series[(1 - x + x^3)/(1 - x - x^2)^2, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 13 2014 *)

CROSSREFS

Cf. A000045, A001629, A046854, A055245.

Sequence in context: A181844 A162506 A227681 * A089068 A018180 A079735

Adjacent sequences:  A055241 A055242 A055243 * A055245 A055246 A055247

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, May 10 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 22 15:16 EDT 2018. Contains 315270 sequences. (Running on oeis4.)