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A124788
Triangle read by rows: expansion of (1+x*y)/(1-x^2*y^2-x^3*y^2).
5
1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 0, 0, 3, 3, 1, 0, 0, 0, 0, 0, 0, 1, 3, 4, 1, 0, 0, 0, 0, 0, 0, 0, 1, 6, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 10, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 10, 10, 6
OFFSET
0,20
COMMENTS
Row sums give A000931(n+5). Diagonal sums are A124789.
FORMULA
Number triangle T(n,k) = binomial(floor(k/2),n-k).
Column k has g.f. x^k*(1+x)^floor(k/2). - Paul Barry, Feb 01 2007
EXAMPLE
Triangle begins
1,
0, 1,
0, 0, 1,
0, 0, 1, 1,
0, 0, 0, 1, 1,
0, 0, 0, 0, 2, 1,
0, 0, 0, 0, 1, 2, 1,
0, 0, 0, 0, 0, 1, 3, 1,
0, 0, 0, 0, 0, 0, 3, 3, 1,
0, 0, 0, 0, 0, 0, 1, 3, 4, 1,
0, 0, 0, 0, 0, 0, 0, 1, 6, 4, 1
MAPLE
A124788 := proc(n, k) binomial(floor(k/2), n-k) ; end: for n from 0 to 20 do for k from 0 to n do printf("%d, ", A124788(n, k)) ; od ; od ; # R. J. Mathar, Feb 10 2007
CROSSREFS
Cf. A124745.
Sequence in context: A227839 A291748 A124744 * A284504 A281245 A284499
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Nov 07 2006
EXTENSIONS
More terms from R. J. Mathar, Feb 10 2007
STATUS
approved