This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A140946 #10 Dec 17 2014 06:22:31 %S A140946 1,-2,-1,4,-4,3,-8,8,-8,-5,16,-16,16,-16,11,-32,32,-32,32,-32,-21,64, %T A140946 -64,64,-64,64,-64,43,-128,128,-128,128,-128,128,-128,-85,256,-256, %U A140946 256,-256,256,-256,256,-256,171,-512,512,-512,512,-512,512,-512,512,-512,-341,1024,-1024,1024,-1024,1024 %N A140946 Triangle T(n,k) = (-2)^n*(-1)^k if k<n; T(n,n) = (-1)^(n+1)*A001045(n+1). %C A140946 The sequence appears if the values b(n+1)-2*b(n) are computed from the (flattened) sequence b(.)=A140944. %C A140946 Reading the triangle by rows, taking absolute values and removing duplicates we obtain A112387. %F A140946 T(n,k) = A140944(n,k+1)-2*A140944(n,k), k<n. %F A140946 T(n,n) = A140944(n+1,0) -2*A140944(n,n). %e A140946 1; %e A140946 -2,-1; %e A140946 4,-4,3; %e A140946 -8,8,-8,-5; %e A140946 16,-16,16,-16,11; %e A140946 -32,32,-32,32,-32,-21; %e A140946 64,-64,64,-64,64,-64,43; %e A140946 -128,128,-128,128,-128,128,-128,-85; %t A140946 (* 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 A140946 Cf. A140513, A140589. %K A140946 sign,tabl %O A140946 0,2 %A A140946 _Paul Curtz_, Jul 24 2008 %E A140946 Edited by _R. J. Mathar_, Jul 06 2011