|
%I #11 Jul 22 2015 04:09:34
%S 1,1,1,1,0,1,1,0,2,1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,2,-3,
%T 8,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,-4,17,-32,1
%N Triangle A(n,k) read by rows: A(n,1)=A(n,n)=1 and A(n,k) = A(n-2,k-1) - 2*A(n,k-1) + 1 for 1<k<n.
%C Row sums are 1, 2, 2, 4, 3, 4, 4, 10, 5, -14, 6, 128, 7, -720, 8, 4630, 9, -30194, 10, ...
%F A(n,k) = A(n-2,k-1) - 2*A(n,k-1) + 1.
%e 1;
%e 1, 1;
%e 1, 0, 1;
%e 1, 0, 2, 1;
%e 1, 0, 1, 0, 1;
%e 1, 0, 1, 1, 0, 1;
%e 1, 0, 1, 0, 1, 0, 1;
%e 1, 0, 1, 0, 2, -3, 8, 1;
%e 1, 0, 1, 0, 1, 0, 1, 0, 1;
%e 1, 0, 1, 0, 1, 1, -4, 17, -32, 1;
%p A144451 := proc(n,k)
%p option remember;
%p if k < 1 or k > n then
%p 0 ;
%p elif n = 1 or n=k then
%p 1;
%p else
%p procname(n-2,k-1)-2*procname(n,k-1)+1 ;
%p end if;
%p end proc: # _R. J. Mathar_, Jul 21 2015
%t A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := A[n, k] = A[n - 2, k - 1] - 2*A[n, k - 1] + 1; a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a]
%K tabl,sign,easy
%O 1,9
%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 06 2008
|
