|
| |
|
|
A005557
|
|
Number of walks on square lattice.
(Formerly M5277)
|
|
6
| |
|
|
42, 132, 297, 572, 1001, 1638, 2548, 3808, 5508, 7752, 10659, 14364, 19019, 24794, 31878, 40480, 50830, 63180, 77805, 95004, 115101, 138446, 165416, 196416, 231880, 272272, 318087, 369852, 428127, 493506, 566618, 648128, 738738, 839188, 950257, 1072764
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
|
|
|
FORMULA
| a(n)= A009766(n+5, 5) =(n+1)*binomial(n+10, 4)/5.
G.f.: (42-120*x+135*x^2-70*x^3+14*x^4)/(1-x)^6; numerator polynomial is N(2;4, x) from A062991.
binomial(n,5)-binomial(n,3),n>=9. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 19 2006
|
|
|
MAPLE
| [seq(binomial(n, 5)-binomial(n, 3), n=9..55)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 19 2006
A005557:=(42-120*z+135*z**2-70*z**3+14*z**4)/(z-1)**6; [Conjectured by S. Plouffe in his 1992 dissertation.]
|
|
|
MATHEMATICA
| s1=s2=s3=s4=0; lst={}; Do[a=n+(n+2); s1+=a; s2+=s1; s3+=s2; s4+=s3; If[s4/2>0, AppendTo[lst, s4/2]], {n, -2, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 04 2009]
CoefficientList[Series[(14 z^4 - 70 z^3 + 135 z^2 - 120 z + 42)/(z - 1)^6, {z, 0, 200}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)
|
|
|
CROSSREFS
| Sixth diagonal of Catalan triangle A033184. Sixth column of Catalan triangle A009766.
Sequence in context: A113518 A044293 A044674 * A045088 A002759 A044374
Adjacent sequences: A005554 A005555 A005556 * A005558 A005559 A005560
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms and formula from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 04 2001
|
| |
|
|
