OFFSET
0,8
COMMENTS
The g.f. of column k of array A063265(n,k) is (x^(ceiling(k/6)))*N7(k,x)/(1-x)^(k+1).
The degree sequence for the polynomials N7(n,x) is [0,0,0,0,0,0,0,5,6,6,6,6,6,5,11,...].
All row sums N7(n,1)= 1.
FORMULA
a(n, m)=[x^m]N7(n, x), n, m >= 0, with N7(n, x) = sum(((1-x)^(j-1))*(x^(b(c(n), j)))*N7(n-j, x), j=1..6), N7(n, x)= 1 for n=0..6 and b(c(n), j) := 1 if 1<= j <= c(n) else 0, with c(n) := 5 if mod(n, 6)=0 and c(n) := mod(n, 6)-1 else; hence b(0, j)=0, j=1..6.
EXAMPLE
{1}; {1}; {1}; {1}; {1}; {1}; {1}; {6, -15, 20, -15, 6, -1}; {5, -9, 5, 5, -9, 5, -1}; ...
c=3: b(3,1)=b(3,2)=b(3,3)=1, b(3,j)=0 for j=4,5,6.
N7(8,x)= 5-9*x+5*x^2+5*x^3-9*x^4+5*x^5-x^6.
CROSSREFS
KEYWORD
sign,easy,tabf
AUTHOR
Wolfdieter Lang, Jul 24 2001
STATUS
approved