A067337 Triangle where T(n,k)=2*T(n,k-1)+C(n-1,k)-C(n-1,k-1) and n>=k>=0.

1, 1, 1, 1, 2, 3, 1, 3, 5, 9, 1, 4, 8, 14, 27, 1, 5, 12, 22, 41, 81, 1, 6, 17, 34, 63, 122, 243, 1, 7, 23, 51, 97, 185, 365, 729, 1, 8, 30, 74, 148, 282, 550, 1094, 2187, 1, 9, 38, 104, 222, 430, 832, 1644, 3281, 6561, 1, 10, 47, 142, 326, 652, 1262, 2476, 4925, 9842

Offset

0,5

Links

Table of n, a(n) for n=0..64.

Formula

T(n, k)=2*T(n, k-1)+A037012(n, k). T(n, k)=T(n-1, k-1)+T(n-1, k) if k<n. T(n, n)=Sum_{j<n}T(n, j)=3^(n-1) if n>0.

Example

Rows start 1; 1,1; 1,2,3; 1,3,5,9; 1,4,8,14,27; etc. T(4,0)=2*0+1-0=1; T(4,1)=2*1+3-1=4; T(4,2)=2*4+3-3=8; T(4,3)=2*8+1-3=14; T(4,4)=2*14+0-1=27.

Crossrefs

Row sums are A025192. Columns include A000012, A000027 and A022856 (essentially). Right hand columns include A000244 (essentially), A007051 and A047926. Central diagonal is A067336.

Sequence in context: A054250 A193923 A198811 * A180091 A047973 A020501

Adjacent sequences: A067334 A067335 A067336 * A067338 A067339 A067340

Keyword

nonn,tabl

Author

Henry Bottomley, Jan 15 2002

Status

approved