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A111518
Sequence is {a(0,n)}, where a(m,0)=1, a(m,n) = a(m-1,n)+a(m,n-1) and a(0,n+1) is such that a(n+1,n+1) = a(0,n).
5
1, 0, -3, -4, 7, 11, -62, -14, 581, -1235, -4175, 32520, -48359, -443625, 3136662, -4834644, -60319241, 506792496, -1210299173, -10327456109, 122982395262, -496826354929, -1709350378156, 39417717346686, -259877263864213, 162788318972691, 14331409095176010
OFFSET
0,3
EXAMPLE
a(0,n): 1,0,-3,-4,7,...
a(1,n): 1,1,-2,-6,1,...
a(2,n): 1,2,0,-6,-5,...
a(3,n): 1,3,3,-3,-8,...
a(4,n): 1,4,7,4,-4,...
Main diagonal is 1,1,0,-3,-4,..., which is 1 followed by sequence a(0,n).
MAPLE
A111518T := proc(nmax) local a, m, n; a := array(0..nmax, 0..nmax) ; for m from 0 to nmax do a[m, 0] := 1 ; od ; for n from 1 to nmax do a[n, n] := a[0, n-1] ; for m from n+1 to nmax do a[m, n] := a[m-1, n]+a[m, n-1] ; od ; for m from n-1 to 0 by -1 do a[m, n] := a[m+1, n]-a[m+1, n-1] ; od ; od ; RETURN(a) ; end: nmax := 50 ; a := A111518T(nmax) ; r := 0 ; for n from 0 to nmax do printf("%d, ", a[r, n]) ; od; # R. J. Mathar, Sep 26 2006
MATHEMATICA
nmax = 26;
a[_, 0] = 1;
a[m_ /; m > 0, n_ /; n > 0] := a[m, n] = a[m - 1, n] + a[m, n - 1];
sol = Solve[Table[a[n + 1, n + 1] == a[0, n], {n, 0, nmax}], Table[a[0, n], {n, 1, nmax+1}], Integers] // First;
Do[a[m, n] = a[m, n] /. sol, {m, 0, nmax}, {n, 0, nmax}];
Table[a[0, n], {n, 0, nmax}] (* Jean-François Alcover, Sep 21 2020 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Leroy Quet, Aug 05 2005
EXTENSIONS
More terms from R. J. Mathar, Sep 26 2006
STATUS
approved