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 A328696 Rectangular array R read by descending antidiagonals:  apply x -> (x+1)/2 to each odd term of the Wythoff array (A035513), and delete all others. 3
 1, 2, 4, 3, 6, 5, 7, 15, 8, 12, 11, 24, 20, 19, 9, 28, 62, 32, 49, 23, 10, 45, 100, 83, 79, 37, 16, 13, 117, 261, 134, 206, 96, 41, 21, 14, 189, 422, 350, 333, 155, 66, 54, 36, 25, 494, 1104, 566, 871, 405, 172, 87, 58, 40, 17, 799, 1786, 1481, 1409, 655 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Every positive integer occurs exactly once in R, and every row of R is a linear recurrence sequence. LINKS EXAMPLE Row 1 of the Wythoff array is (1,2,3,5,8,13,21,34,55,89,144,...), so that row 1 of R is (1,2,3,7,11,...) = A107857 (essentially). _______________ Northwest corner of R:    1,  2,  3,  7,  11,  28,  45,  117,  189,  494,   799    4,  6, 15, 24,  62, 100, 261,  422, 1104, 1786,  4675    5,  8, 20, 32,  83, 134, 350,  566, 1481, 2396,  6272   12, 19, 49, 79, 206, 333, 871, 1409, 3688, 5967, 15621    9, 23, 37, 96, 155, 405, 655, 1714, 2773, 7259, 11745   10, 16, 41, 66, 172, 278, 727, 1176, 3078, 4980, 13037   13, 21, 54, 87, 227, 367, 960, 1553, 4065, 6577, 17218 MATHEMATICA w[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k]; Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten; q[n_, k_] := If[Mod[w[n, k], 2] == 1, (1 + w[n, k])/2, 0]; t[n_] := Union[Table[q[n, k], {k, 1, 50}]]; u[n_] := If[First[t[n]] == 0, Rest[t[n]], t[n]] s = Select[Range[40], ! u[#] == {} &]; u1[n_] := u[s[[n]]]; Column[Table[u1[n], {n, 1, 10}]] (* A328696 array *) v[n_, k_] := u1[n][[k]]; Table[v[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A328696 sequence *) CROSSREFS Cf. A035513, A107857, A328695, A328697. Sequence in context: A255551 A332072 A330340 * A053629 A227370 A135761 Adjacent sequences:  A328693 A328694 A328695 * A328697 A328698 A328699 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Oct 26 2019 STATUS approved

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Last modified June 22 01:06 EDT 2021. Contains 345367 sequences. (Running on oeis4.)