OFFSET
0,8
LINKS
Alex Fink, Richard K. Guy, and Mark Krusemeyer, Partitions with parts occurring at most thrice, Contributions to Discrete Mathematics, Vol 3, No 2 (2008), pp. 76-114.
FORMULA
Recurrence: T(r, 1) = 1, T(r, 2) = -r-1, T(r, c) = -rT(r, c-1) - T(r, c-2). (Corrected Oct 19 2004)
EXAMPLE
Array begins
1, 0, -1, -1, 0, 1, 1, 0, -1, ...
1, -1, -1, 1, 1, -1, -1, 1, 1, ...
1, -2, 1, 1, -2, 1, 1, -2, 1, ...
1, -3, 5, -7, 9, -11, 13, -15, ...
1, -4, 11, -29, 76, -199, 521, ...
1, -5, 19, -71, 265, -989, 3691, ...
...
MATHEMATICA
T[r_, 1] := 1; T[r_, 2] := -r - 1; T[r_, c_] := -r*T[r, c - 1] - T[r, c - 2]; Flatten[ Table[ T[n - i, i], {n, 0, 11}, {i, n + 1}]] (* Robert G. Wilson v, May 10 2005 *)
PROG
(PARI) { t(r, c)=if(c>r||c<0||r<0, 0, if(c>=r-1, (-1)^r*if(c==r, 1, -c), if(r==1, 0, if(c==0, t(r-1, 0)-t(r-2, 0), t(r-1, c)-t(r-2, c)-t(r-1, c-1))))) } T(r, c)=sum(i=0, c, t(c, i)*r^i)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Ralf Stephan, Sep 12 2004
EXTENSIONS
More terms from Robert G. Wilson v, May 10 2005
STATUS
approved