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A175685
Array a(n,m) = Sum_{j=floor((n-1)/2)-m..floor(n-1)/2} binomial(n-j-1,j) read by antidiagonals.
3
1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 3, 2, 1, 1, 3, 4, 3, 2, 1, 1, 1, 7, 5, 3, 2, 1, 1, 4, 7, 8, 5, 3, 2, 1, 1, 1, 14, 12, 8, 5, 3, 2, 1, 1
OFFSET
1,7
COMMENTS
A102426 defines an array of binomials in which partial sums of row n yield row a(n,.).
REFERENCES
Burton, David M., Elementary number theory, McGraw Hill, N.Y., 2002, p. 286.
EXAMPLE
a(n,m) starts in row n=1 as
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...
2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, ...
1, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, ...
3, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, ...
1, 7, 12, 13, 13, 13, 13, 13, 13, 13, 13, ...
4, 14, 20, 21, 21, 21, 21, 21, 21, 21, 21, ...
1, 11, 26, 33, 34, 34, 34, 34, 34, 34, 34, ...
MAPLE
A175685 := proc(n, m) upl := floor( (n-1)/2) ; add( binomial(n-j-1, j), j=upl-m .. upl) ; end proc: # R. J. Mathar, Dec 05 2010
MATHEMATICA
a = Table[Table[Sum[Binomial[n -j - 1, j], {j, Floor[(n - 1)/2] - m, Floor[(n - %t 1)/2]}], {n, 0, 10}], {m, 0, 10}];
Table[Table[a[[m, n - m + 1]], {m, 1, n - 1}], {n, 1, 10}]; Flatten[%]
CROSSREFS
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Dec 04 2010
STATUS
approved