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A192990 Pyramid P(n, t, d) read by planes and rows, for 0 <= t+d <= n: number of ways n triples can sit in a row so that exactly t triples are together and exactly d triples are separated into a couple and a loner. 4
1, 0, 0, 6, 72, 144, 288, 0, 144, 72, 37584, 95904, 98496, 51840, 11664, 25920, 31104, 1296, 7776, 1296, 53529984, 127899648, 130761216, 69921792, 17915904, 11321856, 26002944, 23887872, 10202112, 1430784, 2985984, 2612736, 124416, 373248, 31104 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The plane P(n,,) contains (n+1)*(n+2)/2 numbers.

The row P(n,t,) contains n+1-t numbers.

P(n,t,d) = a((n+1)*(n+2)*(n+3)/6 - (n-t+1)*(n-t+2)/2 + d)

The plane P(n,,) sums to (3n)!

LINKS

Andrew Woods, Table of n, a(n) for n = 0..1770, i.e. from P(0,,) to P(20,,)

EXAMPLE

Pyramid starts:

1...0 0...72 144 288...37584 95904 98496 51840

....6..... 0 144.......11664 25920 31104

..........72........... 1296  7776

....................... 1296

There are P(3,1,2) = 31104 ways to arrange three sets of triples in a row so that one is together and two are split into a couple and a loner.

CROSSREFS

P(n,0,0) = A193624(n).

Sequence in context: A340506 A338535 A250071 * A276244 A282817 A274955

Adjacent sequences:  A192987 A192988 A192989 * A192991 A192992 A192993

KEYWORD

nonn,tabf

AUTHOR

Andrew Woods, Aug 02 2011

STATUS

approved

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Last modified October 22 22:35 EDT 2021. Contains 348180 sequences. (Running on oeis4.)