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A192990
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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.
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4
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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
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OFFSET
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0,4
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COMMENTS
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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)!
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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