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 A202503 Fibonacci self-fission matrix, by antidiagonals. 6
 1, 1, 2, 2, 3, 3, 3, 5, 5, 5, 5, 8, 9, 8, 8, 8, 13, 14, 15, 13, 13, 13, 21, 23, 24, 24, 21, 21, 21, 34, 37, 39, 39, 39, 34, 34, 34, 55, 60, 63, 64, 63, 63, 55, 55, 55, 89, 97, 102, 103, 104, 102, 102, 89, 89, 89, 144, 157, 165, 167, 168, 168, 165, 165, 144, 144, 144 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The Fibonacci self-fission matrix, F, is the fission P^^Q, where P and Q are the matrices given at A202502 and A202451.  See A193842 for the definition of fission. antidiagonal sums:  (1,3,8,18,38,...), A064831 diagonal (1,5,14,39,...), A119996 diagonal (2,8,23,63,...), A180664 diagonal (2,5,15,39,...), A059840 diagonal (3,8,24,63,...), A080097 diagonal (5,13,39,102,...), A080143 diagonal (8,21,63,165,...), A080144 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 EXAMPLE Northwest corner: 1....1....2....3....5.....8....13...21 2....3....5....8...13....21....34...55 3....5....9...14...23....37....60...97 5....8...15...24...39....63...102...165 8...13...24...39...64...103...167...270 MATHEMATICA n = 14; Q = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[Fibonacci[k], {k, 1, n}]]; Qt = Transpose[Q]; P1 = Qt - IdentityMatrix[n]; P = P1[[Range[2, n], Range[1, n]]]; F = P.Q; Flatten[Table[P[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202502 as a sequence *) Flatten[Table[Q[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202451 as a sequence *) Flatten[Table[F[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202503 as a sequence *) TableForm[P]  (* A202502, modified lower triangular Fibonacci array *) TableForm[Q]  (* A202451, upper tri. Fibonacci array *) TableForm[F]  (* A202503, Fibonacci fission array *) CROSSREFS Cf. A202453, A202502, A202451, A000045. Sequence in context: A076272 A180101 A108035 * A049747 A260684 A029093 Adjacent sequences:  A202500 A202501 A202502 * A202504 A202505 A202506 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Dec 20 2011 STATUS approved

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Last modified November 17 22:58 EST 2018. Contains 317279 sequences. (Running on oeis4.)