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A328695 Rectangular array R read by descending antidiagonals: divide to each even term of the Wythoff array (A035513) by 2, and delete all others.

%I A328695 #10 Oct 31 2019 21:42:40
%S A328695 1,4,2,17,9,3,72,38,5,12,305,161,8,51,6,1292,682,13,216,10,7,5473,
%T A328695 2889,21,915,16,30,14,23184,12238,34,3876,26,127,59,25,98209,51841,55,
%U A328695 16419,42,538,250,106,11,416020,219602,89,69552,68,2279,1059,449,18,33
%N A328695 Rectangular array R read by descending antidiagonals:  divide to each even term of the Wythoff array (A035513) by 2, and delete all others.
%C A328695 Every positive integer occurs exactly once in R, and every row of R is a linear recurrence sequence.  The appearance of a sequence s(r) below means that corresponding row of R is the same as s(r) except possibly for one or more initial terms of s(r).
%C A328695 Row 1 of R: A001076
%C A328695 Row 2 of R: A001077
%C A328695 Row 3 of R: A000045
%C A328695 Row 4 of R: A115179
%C A328695 Row 5 of R: A006355
%C A328695 Row 6 of R: A097924
%C A328695 Row 8 of R: A048875
%C A328695 Row 9 of R: A000032
%e A328695 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 (1,4,17,72,...).
%e A328695 _______________
%e A328695 Northwest corner of R:
%e A328695    1   4   17   72  305  1292   5473
%e A328695    2   9   38  161  682  2889  12238
%e A328695    3   5    8   13   21    34     55
%e A328695   12  51  216  915 3876 16419  69552
%e A328695    6  10   16   26   42    68    110
%e A328695    7  30  127  538 2279  9654  40895
%t A328695 w[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];
%t A328695 Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten;
%t A328695 q[n_, k_] := If[Mod[w[n, k], 2] == 0, w[n, k]/2, 0];
%t A328695 t[n_] := Union[Table[q[n, k], {k, 1, 50}]];
%t A328695 u[n_] := If[First[t[n]] == 0, Rest[t[n]], t[n]]
%t A328695 Table[u[n], {n, 1, 10}] (* A328695 array *)
%t A328695 v[n_, k_] := u[n][[k]];
%t A328695 Table[v[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A328695 sequence *)
%Y A328695 Cf. A035513, A001076, A001077, A000045, A115179, A006355, A097924, A048875, A000032, A328696, A328697.
%K A328695 nonn,tabl
%O A328695 1,2
%A A328695 _Clark Kimberling_, Oct 26 2019