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 A141751 Triangle, read by rows, where T(n,k) = [T(n-1,k-1)*T(n-1,k) + 1]/T(n-2,k-1) for 0=0 and T(n,0) = Fibonacci(2*n-1) for n>=1. 2
 1, 1, 1, 2, 2, 1, 5, 5, 3, 1, 13, 13, 8, 4, 1, 34, 34, 21, 11, 5, 1, 89, 89, 55, 29, 14, 6, 1, 233, 233, 144, 76, 37, 17, 7, 1, 610, 610, 377, 199, 97, 45, 20, 8, 1, 1597, 1597, 987, 521, 254, 118, 53, 23, 9, 1, 4181, 4181, 2584, 1364, 665, 309, 139, 61, 26, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS FORMULA T(n,k) = Fibonacci(2*(n-k)-1) + k*Fibonacci(2*(n-k)) for 0<=k<=n. EXAMPLE Generating rule. Given nonzero elements W, X, Y, Z, relatively arranged like so: .. W ..... .. X Y ... .... Z ... then Z = (X*Y + 1)/W. Triangle begins: 1; 1, 1; 2, 2, 1; 5, 5, 3, 1; 13, 13, 8, 4, 1; 34, 34, 21, 11, 5, 1; 89, 89, 55, 29, 14, 6, 1; 233, 233, 144, 76, 37, 17, 7, 1; 610, 610, 377, 199, 97, 45, 20, 8, 1; 1597, 1597, 987, 521, 254, 118, 53, 23, 9, 1; 4181, 4181, 2584, 1364, 665, 309, 139, 61, 26, 10, 1; ... PROG (PARI) T(n, k)=if(n

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Last modified January 17 22:44 EST 2019. Contains 319251 sequences. (Running on oeis4.)