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A123736 Triangle T(n,m)= sum_{j=0..m/2} binomial(n-j-1,m-2j), read by rows. 3
1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 1, 0, 1, 3, 4, 3, 2, 1, 1, 0, 1, 4, 7, 7, 5, 3, 2, 1, 1, 0, 1, 5, 11, 14, 12, 8, 5, 3, 2, 1, 1, 0, 1, 6, 16, 25, 26, 20, 13, 8, 5, 3, 2, 1, 1, 0, 1, 7, 22, 41, 51, 46, 33, 21, 13, 8, 5, 3, 2, 1, 1, 0, 1, 8, 29, 63, 92, 97, 79, 54, 34, 21, 13, 8, 5, 3, 2, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Row sums give: A000225

LINKS

Table of n, a(n) for n=1..91.

Eric Weisstein's World of Mathematics, Steenrod Algebra

EXAMPLE

The triangle starts in row n=1 with columns 0<=m<2*n:

{1, 0},

{1, 1, 1, 0},

{1, 2, 2, 1, 1, 0},

{1, 3, 4, 3, 2, 1, 1, 0},

{1, 4, 7, 7, 5, 3, 2, 1, 1, 0},

{1, 5, 11, 14, 12, 8, 5, 3, 2, 1, 1, 0},

{1, 6, 16, 25, 26, 20, 13, 8, 5, 3, 2, 1, 1, 0},

{1, 7, 22, 41, 51, 46, 33, 21, 13, 8, 5, 3, 2, 1, 1, 0},

{1, 8, 29, 63, 92, 97, 79, 54, 34, 21, 13, 8, 5, 3, 2, 1, 1, 0},

{1, 9, 37, 92, 155, 189, 176, 133, 88, 55, 34, 21, 13, 8, 5, 3, 2, 1, 1, 0}

MATHEMATICA

a = Table[Table[Sum[Binomial[j - k - 1, i - 2*k], {k, 0, i}], {i, 0, 2*j - 1}], {j, 0, 10}]; Join[{{0}}, a]; Flatten[a]

CROSSREFS

Cf. A136431 (antidiagonals), A027926 (row-reversed), A004006 (column m=3)

Sequence in context: A282750 A265890 A226920 * A185304 A081389 A133685

Adjacent sequences:  A123733 A123734 A123735 * A123737 A123738 A123739

KEYWORD

nonn,easy,tabf

AUTHOR

Roger L. Bagula, Nov 14 2006

STATUS

approved

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Last modified November 17 00:02 EST 2018. Contains 317275 sequences. (Running on oeis4.)