%I A059116
%S A059116 0,0,6,114,978,6810,43746,271194,1653378,9998970,60229986,362088474,
%T A059116 2174656578,13054316730,78345032226,470127588954,2820937720578
%N A059116 The sequence lambda(4,n), where lambda is defined in A055203. Number 
               of ways of placing n identifiable positive intervals with a total 
               of exactly four starting and/or finishing points.
%C A059116 For all n, a(n)=1*6^n-4*3^n+6*1^n-4*0^n+1*0^n [with 0^0=1] where powers 
               are taken of triangular numbers and multiplied by binomial coefficients 
               with alternating signs.
%F A059116 For n>0, a(n) =6^n-4*3^n+6.
%e A059116 a(2)=6 since intervals a-a and b-b can be combined as a-a-b-b, a-b-a-b, 
               a-b-b-a, b-a-b-a, b-a-a-b, or b-a-a-b.
%Y A059116 Cf. A058809, A059117.
%Y A059116 Sequence in context: A088668 A066931 A051228 this_sequence A121544 A003425 
               A052465
%Y A059116 Adjacent sequences: A059113 A059114 A059115 this_sequence A059117 A059118 
               A059119
%K A059116 nonn
%O A059116 0,3
%A A059116 Henry Bottomley (se16(AT)btinternet.com), Jan 05 2001