A117389 A skew Delannoy number triangle read by rows.

1, 0, 1, 0, 1, 1, 0, 0, 3, 1, 0, 0, 1, 5, 1, 0, 0, 0, 5, 7, 1, 0, 0, 0, 1, 13, 9, 1, 0, 0, 0, 0, 7, 25, 11, 1, 0, 0, 0, 0, 1, 25, 41, 13, 1, 0, 0, 0, 0, 0, 9, 63, 61, 15, 1, 0, 0, 0, 0, 0, 1, 41, 129, 85, 17, 1

Offset

0,9

Comments

Row sums are the trinomial numbers A000073(n+2). Diagonal sums are A079973.

Links

Table of n, a(n) for n=0..65.

Formula

Number triangle T(n,k)=[k<=n]*sum{j=0..2k-n, C(2k-n,j)C(n-k,j)2^j}; T(n,k)=sum{j=0..2k-n, C(2k-n,j)C(n-k,n-k-j)2^j};

Example

Triangle begins
1,
0, 1,
0, 1, 1,
0, 0, 3, 1,
0, 0, 1, 5, 1,
0, 0, 0, 5, 7, 1,
0, 0, 0, 1, 13, 9, 1,
0, 0, 0, 0, 7, 25, 11, 1

Crossrefs

Cf. A008288.

Sequence in context: A342270 A330248 A247505 * A122083 A098158 A110319

Adjacent sequences: A117386 A117387 A117388 * A117390 A117391 A117392

Keyword

easy,nonn,tabl

Author

Paul Barry, Mar 11 2006

Status

approved