A167666 Triangle read by rows given by [1,1,-4,2,0,0,0,0,0,0,0,...] DELTA [1,0,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

1, 1, 1, 2, 3, 1, 0, 4, 5, 1, 0, 0, 6, 7, 1, 0, 0, 0, 8, 9, 1, 0, 0, 0, 0, 10, 11, 1, 0, 0, 0, 0, 0, 12, 13, 1, 0, 0, 0, 0, 0, 0, 14, 15, 1, 0, 0, 0, 0, 0, 0, 0, 16, 17, 1, 0, 0, 0, 0, 0, 0, 0, 0, 18, 19, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 21, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 23, 1, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,4

Comments

Row sums = A111284(n+1), Diagonal sums = A109613(n).

Links

Table of n, a(n) for n=0..98.

Formula

T(n,k) = 2*T(n-1,k-1) - T(n-2,k-2), T(0,0) = T(1,0) = T(1,1) = 1, T(2,0) = 2, T(2,1) = 3, T(3,0) = 0, T(3,1) = 4. - Philippe Deléham, Feb 18 2012

G.f.: (1+(1-y)*x+(2+y)*x^2)/(1-y*x)^2. - Philippe Deléham, Feb 18 2012

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A130779(n), A111284(n+1), A167667(n), A167682(n) for x = -1, 0, 1, 2, 3 respectively. - Philippe Deléham, Feb 18 2012

Example

Triangle begins :
1 ;
1, 1 ;
2, 3, 1 ;
0, 4, 5, 1 ;
0, 0, 6, 7, 1 ;
0, 0, 0, 8, 9, 1 ;
0, 0, 0, 0, 10, 11, 1 ; ...

Crossrefs

Cf. A000012, A005408, A005843

Sequence in context: A368486 A178245 A338753 * A115352 A275808 A038554

Adjacent sequences: A167663 A167664 A167665 * A167667 A167668 A167669

Keyword

nonn,tabl

Author

Philippe Deléham, Nov 08 2009

Status

approved