%I A007574 M2653
%S A007574 1,3,7,15,31,60,113,207,373,663,1167,2038,3537,6107,10499,
%T A007574 17983,30703,52272,88769,150407,254321,429223,723167,1216490,
%U A007574 2043361,3427635,5742463,9609327,16062463,26821668,44744657
%N A007574 Patterns in a dual ring.
%D A007574 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007574 C. A. Church, Jr., Lattice paths and Fibonacci and Lucas numbers, Fibonacci 
               Quarterly 12(4) (1974) 336-338.
%D A007574 W. Dotson, F. Norwood and C. Taylor, Fiber optics and Fibonacci, Math. 
               Mag., 66 (1993), 167-174.
%p A007574 with(combinat): A007574 := proc(n) local k; if n=1 then RETURN(1) fi; 
               if n=2 then RETURN(3) fi; if n=3 then RETURN(7) fi; if n>3 then RETURN( 
               fibonacci(n)+2*fibonacci(n-1)+n*sum(fibonacci(n-k),k=2..n-1)) fi; 
               end;
%t A007574 Table[ Fibonacci[n] + 2 Fibonacci[n - 1] + n*Sum[Fibonacci[n - k], {k, 
               2, n - 1}], {n, 1, 35} ]
%Y A007574 Cf. A000045.
%Y A007574 Sequence in context: A151338 A023424 A006778 this_sequence A034480 A057703 
               A006739
%Y A007574 Adjacent sequences: A007571 A007572 A007573 this_sequence A007575 A007576 
               A007577
%K A007574 nonn
%O A007574 1,2
%A A007574 Simon Plouffe, N. J. A. Sloane (njas(AT)research.att.com), Robert G. 
               Wilson v (rgwv(AT)rgwv.com)