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 A202453 Fibonacci self-fusion matrix, by antidiagonals. 65
 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 5, 5, 6, 5, 5, 8, 8, 9, 9, 8, 8, 13, 13, 15, 15, 15, 13, 13, 21, 21, 24, 24, 24, 24, 21, 21, 34, 34, 39, 39, 40, 39, 39, 34, 34, 55, 55, 63, 63, 64, 64, 63, 63, 55, 55, 89, 89, 102, 102, 104, 104, 104, 102, 102, 89, 89, 144, 144, 165, 165 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The Fibonacci self-fusion matrix, F, is the fusion P**Q, where P and Q are the lower and upper triangular Fibonacci matrices.  See A193722 for the definition of fusion of triangular arrays. Every term F(n,k) of F is a product of two Fibonacci numbers; indeed, F(n,k)=F(n)*F(k+1) if k is even; F(n,k)=F(n+1)*F(k) if k is odd. antidiagonal sums: (1,2,6,12,...), A054454 diagonal (1,2,6,15,...), A001654 diagonal (1,3,9,24,...), A064831 diagonal (2,5,15,39,..), A059840 diagonal (3,8,24,63,..), A080097 diagonal (5,13,39,102,...), A080143 diagonal (8,21,63,165,...), A080144 principal submatrix sums, A202462 All the principal submatrices are invertible, and the terms in the inverses are in {-3,-2,-1,0,1,2,3}. REFERENCES C. Kimberling, Fusion, Fission, and Factors, Fib. Q., 52 (2014), 195-202. LINKS FORMULA Matrix product P*Q, where P, Q are the lower and upper triangular Fibonacci matrices, A202451 and A202452. EXAMPLE Northwest corner: 1...1....2....3....5....8....13 1...2....3....5....8...13....21 2...3....6....9...15...24....39 3...5....9...15...24...39....63 5...8...15...24...40...64...104 MATHEMATICA n = 12; Q = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[Fibonacci[k], {k, 1, n}]]; P = Transpose[Q]; F = P.Q; Flatten[Table[P[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202452 as a sequence *) Flatten[Table[Q[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202451 as a sequence *) Flatten[Table[F[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202453 as a sequence *) TableForm[Q]  (* A202451, upper tri. Fibonacci array *) TableForm[P]  (* A202452, lower tri. Fibonacci array *) TableForm[F]  (* A202453, Fibonacci fusion array *) TableForm[FactorInteger[F]] CROSSREFS Cf. A000045, A202451, A202452, A202503 (Fibonacci fission array). Sequence in context: A237050 A235130 A131410 * A259529 A196052 A080773 Adjacent sequences:  A202450 A202451 A202452 * A202454 A202455 A202456 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Dec 19 2011 STATUS approved

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