OFFSET
0,4
COMMENTS
The Comtet formula for I(n) = round(9*n^2+18-n*b(n)/16) with b(n)=bar(7,4,1,10) with period 4, is missing divisors (32?) somewhere.
REFERENCES
L. Comtet, Advanced Combinatorics (Reidel, 1974), page 122, exercise 19 sequence (2).
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-2,0,0,-1,1).
FORMULA
G.f.: -x^2*(x^2 - x + 1)*(x^5 + x^4 + x^3 + 2*x^2 + 3*x + 1) / ( (1+x)^2*(x^2+1)^2*(x-1)^3 ).
EXAMPLE
The 3 solutions for n=3 or n=4 are (x,y)=(1,0), (1,1), (2,0).
MAPLE
A056594 := proc(n)
if type (n, 'odd') then
0;
else
(-1)^(n/2) ;
end if;
end proc:
A008619 := proc(n)
1+iquo(n, 2) ;
end proc:
A321986 := proc(n)
if n =0 then
0;
else
-11*n +35/2 +9*n^2 +9/2*(-1)^n -3*(-1)^n*n +22*A056594(n) -2*A056594(n-1) +12*(-1)^A008619(n)*A008619(n) ;
%/32 ;
end if;
end proc:
seq(A321986(n), n=0..30) ;
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
R. J. Mathar, Nov 23 2018
STATUS
approved