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A224838 Triangle of falling diagonals of A011973 (with rows displayed as centered text). 3
1, 1, 1, 2, 1, 1, 3, 1, 1, 3, 4, 1, 4, 6, 5, 1, 1, 10, 10, 6, 1, 1, 5, 20, 15, 7, 1, 6, 15, 35, 21, 8, 1, 1, 21, 35, 56, 28, 9, 1, 1, 7, 56, 70, 84, 36, 10, 1, 8, 28, 126, 126, 120, 45, 11, 1, 1, 36, 84, 252, 210, 165, 55, 12, 1, 1, 9, 120, 210, 462, 330, 220, 66, 13, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row sums are A005314 with offset = 1.

LINKS

Table of n, a(n) for n=1..75.

FORMULA

r(n) = binomial(n-floor((4n+15-6k+(-1)^k)/12), n-floor((4n+15-6k+(-1)^k)/12)-floor((2n-1)/3)+k-1), {k,1,floor((2n+2)/3)}.

R(n) = binomial(n-Floor((k+1)/2), n-Floor((3k-1)/2)), {k,1,floor((2n+2)/3)} - gives the terms of each row in reverse order.

EXAMPLE

First 11 triangle rows are :

1

1,  1

2,  1

1,  3,  1

1,  3,  4,  1

4,  6,  5,  1

1, 10, 10,  6,  1

1,  5, 20, 15,  7,  1

6, 15, 35, 21,  8,  1

1, 21, 35, 56, 28,  9,  1

1,  7, 56, 70, 84, 36, 10,  1

MATHEMATICA

Table[Reverse[Table[Binomial[n - Floor[(k + 1)/2], n - Floor[(3 k - 1)/2]], {k, Floor[(2 n + 2)/3]}]], {n, 13}] (* T. D. Noe, Jul 25 2013 *)

Column[Table[Binomial[n - Floor[(4 n + 15 - 6 k + (-1)^k)/12], n - Floor[(4 n + 15 - 6 k + (-1)^k)/12] - Floor[(2 n - 1)/3] + k - 1], {n, 1, 25}, {k, 1, Floor[(2 n + 2)/3]}]] (* John Molokach, Jul 25 2013 *)

CROSSREFS

Cf. A005314, A227300, A001973, A000045, A004396.

Sequence in context: A181846 A305499 A210873 * A030272 A157128 A301376

Adjacent sequences:  A224835 A224836 A224837 * A224839 A224840 A224841

KEYWORD

nonn,tabf

AUTHOR

John Molokach, Jul 21 2013

STATUS

approved

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Last modified March 29 18:37 EDT 2020. Contains 333117 sequences. (Running on oeis4.)