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A098495
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Array T(r,c) read by antidiagonals: values of triangle A098493 interpreted as polynomials, r>=0.
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4
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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REFERENCES
| A. Fink, R. K. Guy and M. Krusemeyer, Partitions with parts occurring at most thrice, in preparation.
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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)
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EXAMPLE
| 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,
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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}]] (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 10 2005)
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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)
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CROSSREFS
| See A094954 (with negative k) for negative r and more formulae 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
Adjacent sequences: A098492 A098493 A098494 * A098496 A098497 A098498
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KEYWORD
| sign,tabl
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AUTHOR
| Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 12 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 10 2005
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