A140946 - OEIS

%I #10 Dec 17 2014 06:22:31

%S 1,-2,-1,4,-4,3,-8,8,-8,-5,16,-16,16,-16,11,-32,32,-32,32,-32,-21,64,

%T -64,64,-64,64,-64,43,-128,128,-128,128,-128,128,-128,-85,256,-256,

%U 256,-256,256,-256,256,-256,171,-512,512,-512,512,-512,512,-512,512,-512,-341,1024,-1024,1024,-1024,1024

%N Triangle T(n,k) = (-2)^n*(-1)^k if k<n; T(n,n) = (-1)^(n+1)*A001045(n+1).

%C The sequence appears if the values b(n+1)-2*b(n) are computed from the (flattened) sequence b(.)=A140944.

%C Reading the triangle by rows, taking absolute values and removing duplicates we obtain A112387.

%F T(n,k) = A140944(n,k+1)-2*A140944(n,k), k<n.

%F T(n,n) = A140944(n+1,0) -2*A140944(n,n).

%e 1;

%e -2,-1;

%e 4,-4,3;

%e -8,8,-8,-5;

%e 16,-16,16,-16,11;

%e -32,32,-32,32,-32,-21;

%e 64,-64,64,-64,64,-64,43;

%e -128,128,-128,128,-128,128,-128,-85;

%t (* A = A140944 *) A[0, 0] = 0; A[1, 0] = A[0, 1] = 1; A[0, k_] := A[0, k] = A[0, k-1] + 2*A[0, k-2]; A[n_, n_] = 0; A[n_, k_] := A[n, k] = A[n-1, k+1] - A[n-1, k];  T[n_, n_] := T[n, n] = A[n+1, 0] - 2*A[n, n]; T[n_, k_] := T[n, k] = A[n, k+1] - 2*A[n, k]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Dec 17 2014 *)

%Y Cf. A140513, A140589.

%K sign,tabl

%O 0,2

%A _Paul Curtz_, Jul 24 2008

%E Edited by _R. J. Mathar_, Jul 06 2011