A119865 Triangle T(n,k), 0<=k<=n, read by rows, given by [1, 1, 0, 1, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.

1, 1, 1, 2, 3, 1, 4, 9, 6, 1, 8, 25, 26, 10, 1, 16, 65, 95, 60, 15, 1, 32, 161, 308, 279, 120, 21, 1, 64, 385, 917, 1099, 693, 217, 28, 1, 128, 897, 2566, 3856, 3256, 1526, 364, 36, 1

Offset

0,4

Links

Table of n, a(n) for n=0..44.

Formula

Sum_{k =0..n}T(n,k)= A087944(n).

Sum_{k=0..n}(-1)^k*2^(n-k)*T(n,k)= n^2-n+1= A002061(n).

Sum_{k=0..n}(-1)^k*T(n,k)=0^n= A000007(n).

G.f.: (1-2*x-2*x*y++x^2+x^2*y+x^2*y^2)/(1-3*x-3*x*y+2*x^2+4*x^2*y+3*x^2*y^2-x^3*y^2-x^3*y^3). - Philippe Deléham, Nov 09 2013

T(n,k) = 3*T(n-1,k) + 3*T(n-1,k-1) - 2*T(n-2,k) - 4*T(n-2,k-1) - 3*T(n-2,k-2) + T(n-3,k-2) + T(n-3,k-3), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = 2, T(2,1) = 3, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Nov 09 2013

Example

Triangle begins:
1;
1, 1;
2, 3, 1;
4, 9, 6, 1;
8, 25, 26, 10, 1;
16, 65, 95, 60, 15, 1;
32, 161, 308, 279, 120, 21, 1;
64, 385, 917, 1099, 693, 217, 28, 1;
128, 897, 2566, 3856, 3256, 1526, 364, 36, 1;

Crossrefs

Cf. Diagonals : A011782, A002064 ; A000012, A000217.

Sequence in context: A358664 A231206 A165241 * A177896 A193920 A076732

Adjacent sequences: A119862 A119863 A119864 * A119866 A119867 A119868

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Jul 31 2006

Status

approved