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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 (list; table; graph; refs; listen; history; text; internal format)
 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. LINKS 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 Cf. A000045, A011973, A102426. Sequence in context: A207194 A086275 A066855 * A331182 A182591 A321393 Adjacent sequences:  A175682 A175683 A175684 * A175686 A175687 A175688 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula, Dec 04 2010 STATUS approved

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Last modified June 22 12:56 EDT 2021. Contains 345380 sequences. (Running on oeis4.)