Search: id:A098495
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%I A098495
%S A098495 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,
%T A098495 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,
%U A098495 989,521,15,1,1,0,1,10,71,377,1393,3191,3691,1364,17,1,1,1,1,11,89,559
%V A098495 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,
%W A098495 -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,
%X A098495 521,-15,1,-1,0,1,-10,71,-377,1393,-3191,3691,-1364,17,1,-1,1,1,-11,89,
               -559
%N A098495 Array T(r,c) read by antidiagonals: values of triangle A098493 interpreted 
               as polynomials, r>=0.
%D A098495 A. Fink, R. K. Guy and M. Krusemeyer, Partitions with parts occurring 
               at most thrice, in preparation.
%F A098495 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)
%e A098495 1,0,-1,-1,0,1,1,0,-1,
%e A098495 1,-1,-1,1,1,-1,-1,1,1,
%e A098495 1,-2,1,1,-2,1,1,-2,1,
%e A098495 1,-3,5,-7,9,-11,13,-15,
%e A098495 1,-4,11,-29,76,-199,521,
%e A098495 1,-5,19,-71,265,-989,3691,
%t A098495 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)
%o A098495 (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)
%Y A098495 See A094954 (with negative k) for negative r and more formulae and programs.
%Y A098495 Rows include (-1)^c times A005408, A002878, A001834, A030221, A002315. 
               Columns include A028387. Antidiagonal sums are in A098496.
%Y A098495 Sequence in context: A125692 A128258 A104967 this_sequence A095025 A069897 
               A107682
%Y A098495 Adjacent sequences: A098492 A098493 A098494 this_sequence A098496 A098497 
               A098498
%K A098495 sign,tabl
%O A098495 0,8
%A A098495 Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 12 2004
%E A098495 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 10 2005

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