A136482 Triangle read by rows: T(n,k) = 2*A007318(n,k) - A034851(n,k) (i.e., twice Pascal's triangle - the Losanitch triangle).

1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 6, 8, 6, 1, 1, 7, 14, 14, 7, 1, 1, 9, 21, 30, 21, 9, 1, 1, 10, 30, 51, 51, 30, 10, 1, 1, 12, 40, 84, 102, 84, 40, 12, 1, 1, 13, 52, 124, 186, 186, 124, 52, 13, 1, 1, 15, 65, 180, 310, 378, 310, 180, 65, 15, 1, 1, 16, 80, 245, 490, 688, 688, 490, 245

Offset: 0

Author

Gary W. Adamson, Dec 31 2007

Keywords

• nonn
• tabl

Comments

Row sums are apparently in A135098. - R. J. Mathar, May 01 2008

Examples

			Row n=3 is 2*(1,3,3,1) - (1,2,2,1) = (1,4,4,1).
		

Crossrefs

Cf. A007318, A034851, A136489.

Programs

Maple

A007318 := proc(n,k) binomial(n,k) ; end: A051159 := proc(n,k) binomial(n mod 2, k mod 2)*binomial(floor(n/2),floor(k/2)) ; end: A034851 := proc(n,k) (A007318(n,k)+A051159(n,k))/2 ; end: A136482 := proc(n,k) 2*A007318(n,k)-A034851(n,k) ; end: for n from 0 to 13 do for k from 0 to n do printf("%d,",A136482(n,k)) ; od: od: # R. J. Mathar, May 01 2008

Extensions

Edited and corrected by R. J. Mathar, May 01 2008