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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

Table of n, a(n) for n=1..45.

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.)