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A136482
Triangle read by rows: T(n,k) = 2*A007318(n,k) - A034851(n,k) (i.e., twice Pascal's triangle - the Losanitch triangle).
2
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
0,5
COMMENTS
Row sums are apparently in A135098. - R. J. Mathar, May 01 2008
EXAMPLE
Row n=3 is 2*(1,3,3,1) - (1,2,2,1) = (1,4,4,1).
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
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Dec 31 2007
EXTENSIONS
Edited and corrected by R. J. Mathar, May 01 2008
STATUS
approved