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A098495
Array T(r,c) read by antidiagonals: values of triangle A098493 interpreted as polynomials, r >= 0.
5
1, 1, 0, 1, -1, -1, 1, -2, -1, -1, 1, -3, 1, 1, 0, 1, -4, 5, 1, 1, 1, 1, -5, 11, -7, -2, -1, 1, 1, -6, 19, -29, 9, 1, -1, 0, 1, -7, 29, -71, 76, -11, 1, 1, -1, 1, -8, 41, -139, 265, -199, 13, -2, 1, -1, 1, -9, 55, -239, 666, -989, 521, -15, 1, -1, 0, 1, -10, 71, -377, 1393, -3191, 3691, -1364, 17, 1, -1, 1, 1, -11, 89, -559
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
See A094954 (with negative k) for negative r and more formulas and programs.
Rows include (-1)^c times A005408, A002878, A001834, A030221, A002315. Columns include A028387. Antidiagonal sums are in A098496.
Sequence in context: A125692 A128258 A104967 * A175432 A204118 A095025
KEYWORD
sign,tabl
AUTHOR
Ralf Stephan, Sep 12 2004
EXTENSIONS
More terms from Robert G. Wilson v, May 10 2005
STATUS
approved