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 A283845 Square array read by antidiagonals: T(1,1) = T(1,2) = T(2,1) = T(2,2) = 1; thereafter T(m,n) = min {T(m,n-2) + T(m,n-1), T(m-2,n) + T(m-1,n), T(m-2,n-2) + T(m-1,n-1)}. 2
 1, 1, 1, 2, 1, 2, 3, 2, 2, 3, 5, 3, 2, 3, 5, 8, 5, 3, 3, 5, 8, 13, 8, 5, 3, 5, 8, 13, 21, 13, 8, 5, 5, 8, 13, 21, 34, 21, 13, 8, 5, 8, 13, 21, 34, 55, 34, 21, 13, 8, 8, 13, 21, 34, 55, 89, 55, 34, 21, 13, 8, 13, 21, 34, 55, 89, 144, 89, 55, 34, 21, 13, 13, 21, 34, 55, 89, 144 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A naive version of a two-dimensional Fibonacci array. There should probably be another entry for the array which has offset 0 and starts with T(0,0) = 0, T(0,1) = T(1,0) = T(1,1) = 1. See A058071 for a more interesting version. T(n, 1) = T(n, n) = A000045(n) for n > 0. - Indranil Ghosh, Apr 01 2017 LINKS Indranil Ghosh, Rows 1..120, flattened Indranil Ghosh, C program to generate the triangle FORMULA T(m,n) = Fibonacci(k) where k = max(m,n). EXAMPLE The square array begins: 1, 1, 2, 3, 5, 8, 13, 21, ... 1, 1, 2, 3, 5, 8, 13, 21, ... 2, 2, 2, 3, 5, 8, 13, 21, ... 3, 3, 3, 3, 5, 8, 13, 21, ... 5, 5, 5, 5, 5, 8, 13, 21, ... 8, 8, 8, 8, 8, 8, 13, 21, ... 13, 13, 13, 13, 13, 13, 13, 21, ... ... The first few antidiagonals are: 1; 1, 1; 2, 1, 2; 3, 2, 2, 3; 5, 3, 2, 3, 5; 8, 5, 3, 3, 5, 8; 13, 8, 5, 3, 5, 8, 13; ... MATHEMATICA Table[Fibonacci[Max[m, n - m + 1]], {n, 20}, {m, n}] // Flatten (* Indranil Ghosh, Apr 01 2017 *) PROG (PARI) tabl(nn) = {for(n=1, nn, for(m=1, n, print1(fibonacci(max(m, n - m + 1)), ", "); ); print(); ); } tabl(20) \\ Indranil Ghosh, Apr 01 2017 (Python) from sympy import fibonacci for n in range(1, 21): ....print [fibonacci(max(m, n - m + 1)) for m in range(1, n + 1)] # Indranil Ghosh, Apr 01 2017 CROSSREFS Cf. A000045, A058071. Sequence in context: A342859 A342385 A367108 * A365543 A058071 A174961 Adjacent sequences: A283842 A283843 A283844 * A283846 A283847 A283848 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Mar 31 2017 EXTENSIONS Extended by Indranil Ghosh, Apr 01 2017 STATUS approved

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Last modified August 12 10:13 EDT 2024. Contains 375092 sequences. (Running on oeis4.)