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A205456 Symmetric matrix by antidiagonals: C(max(i,j),min(i,j)), i>=1, j>=1. 7
1, 2, 2, 3, 1, 3, 4, 3, 3, 4, 5, 6, 1, 6, 5, 6, 10, 4, 4, 10, 6, 7, 15, 10, 1, 10, 15, 7, 8, 21, 20, 5, 5, 20, 21, 8, 9, 28, 35, 15, 1, 15, 35, 28, 9, 10, 36, 56, 35, 6, 6, 35, 56, 36, 10, 11, 45, 84, 70, 21, 1, 21, 70, 84, 45, 11, 12, 55, 120, 126, 56, 7, 7, 56, 126, 120 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

C(max(i,j),min(i,j))=number of {E,N,NE} paths from (0,0) to (i,j).  Each step of a path is represented by (a,b)->(a+1,b) or (a,b)->(a,b+1) or (a,b)->(a+1,b+1).  To include paths from (0,0) to points (a,0) and (0,b), see A059674.

LINKS

Table of n, a(n) for n=1..76.

EXAMPLE

Northwest corner:

1....2....3....4....5....6....7

2....1....3....6....10...15...21

3....3....1....4....10...20...35

4....6....4....1....5....15...35

5....10...10...5....1....6....21

MATHEMATICA

f[i_, j_] := Binomial[Max[i, j], Min[i, j]]

TableForm[Table[f[i, j], {i, 1, 10}, {j, 1, 10}]]

Flatten[Table[f[i, n + 1 - i], {n, 1, 14}, {i, 1, n}]]

CROSSREFS

Cf. A205457, A205548, A059674.

Sequence in context: A072030 A217029 A331886 * A080045 A191384 A191305

Adjacent sequences:  A205453 A205454 A205455 * A205457 A205458 A205459

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 28 2012

STATUS

approved

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Last modified December 5 10:11 EST 2021. Contains 349543 sequences. (Running on oeis4.)