OFFSET
2,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 2..1000
R. K. Guy, Letter to N. J. A. Sloane, May 1990
R. K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6, w_n'(2).
FORMULA
a(n) = C(n+3, ceiling(n/2))*C(n+2, floor(n/2)) - C(n+3, ceiling((n-1)/2))*C(n+2, floor((n-1)/2)). - Paul D. Hanna, Apr 16 2004
Conjecture: (n-1)*(n-2)*(2*n+1)*(n+5)*(n+4)*a(n) -4*n*(n+1)*(2*n^2+4*n+19)*a(n-1) -16*n^2*(n-1)*(2*n+3)*(n+1)*a(n-2)=0. - R. J. Mathar, Apr 02 2017
MAPLE
wnprime := proc(n, y)
local k;
if type(n-y, 'even') then
k := (n-y)/2 ;
binomial(n+1, k)*(binomial(n, k)-binomial(n, k-1)) ;
else
k := (n-y-1)/2 ;
binomial(n+1, k)*binomial(n, k+1)-binomial(n+1, k+1)*binomial(n, k-1) ;
end if;
end proc:
A005560 := proc(n)
wnprime(n, 2) ;
end proc:
seq(A005560(n), n=2..20) ; # R. J. Mathar, Apr 02 2017
MATHEMATICA
Table[Binomial[n+3, Ceiling[n/2]] Binomial[n+2, Floor[n/2]]-Binomial[n+3, Ceiling[(n-1)/2]] Binomial[n+2, Floor[(n-1)/2]], {n, 0, 30}] (* Vincenzo Librandi, Apr 03 2017 *)
PROG
(PARI) {a(n)=binomial(n+3, ceil(n/2))*binomial(n+2, floor(n/2)) - binomial(n+3, ceil((n-1)/2))*binomial(n+2, floor((n-1)/2))}
(Magma) [Binomial(n+3, Ceiling(n/2))*Binomial(n+2, Floor(n/2)) - Binomial(n+3, Ceiling((n-1)/2))*Binomial(n+2, Floor((n-1)/2)): n in [0..30]]; // Vincenzo Librandi, Apr 03 2017
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
STATUS
approved