A140946 Triangle T(n,k) = (-2)^n*(-1)^k if k<n; T(n,n) = (-1)^(n+1)*A001045(n+1).

1, -2, -1, 4, -4, 3, -8, 8, -8, -5, 16, -16, 16, -16, 11, -32, 32, -32, 32, -32, -21, 64, -64, 64, -64, 64, -64, 43, -128, 128, -128, 128, -128, 128, -128, -85, 256, -256, 256, -256, 256, -256, 256, -256, 171, -512, 512, -512, 512, -512, 512, -512, 512, -512, -341, 1024, -1024, 1024, -1024, 1024

Offset

0,2

Comments

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

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

Links

Table of n, a(n) for n=0..59.

Formula

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

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

Example

1;
-2,-1;
4,-4,3;
-8,8,-8,-5;
16,-16,16,-16,11;
-32,32,-32,32,-32,-21;
64,-64,64,-64,64,-64,43;
-128,128,-128,128,-128,128,-128,-85;

Mathematica

(* 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 *)

Crossrefs

Cf. A140513, A140589.

Sequence in context: A091335 A362865 A274883 * A008741 A369999 A110316

Adjacent sequences: A140943 A140944 A140945 * A140947 A140948 A140949

Keyword

sign,tabl

Author

Paul Curtz, Jul 24 2008

Extensions

Edited by R. J. Mathar, Jul 06 2011

Status

approved