cp's OEIS Frontend

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.

%I A192990 #23 Jan 19 2019 04:14:58
%S A192990 1,0,0,6,72,144,288,0,144,72,37584,95904,98496,51840,11664,25920,
%T A192990 31104,1296,7776,1296,53529984,127899648,130761216,69921792,17915904,
%U A192990 11321856,26002944,23887872,10202112,1430784,2985984,2612736,124416,373248,31104
%N 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.
%C A192990 The plane P(n,,) contains (n+1)*(n+2)/2 numbers.
%C A192990 The row P(n,t,) contains n+1-t numbers.
%C A192990 P(n,t,d) = a((n+1)*(n+2)*(n+3)/6 - (n-t+1)*(n-t+2)/2 + d)
%C A192990 The plane P(n,,) sums to (3n)!
%H A192990 Andrew Woods, <a href="/A192990/b192990.txt">Table of n, a(n) for n = 0..1770</a>, i.e. from P(0,,) to P(20,,)
%e A192990 Pyramid starts:
%e A192990 1...0 0...72 144 288...37584 95904 98496 51840
%e A192990 ....6..... 0 144.......11664 25920 31104
%e A192990 ..........72........... 1296  7776
%e A192990 ....................... 1296
%e A192990 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.
%Y A192990 P(n,0,0) = A193624(n).
%K A192990 nonn,tabf
%O A192990 0,4
%A A192990 _Andrew Woods_, Aug 02 2011