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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. 3
1, 4, 2, 17, 9, 3, 72, 38, 5, 12, 305, 161, 8, 51, 6, 1292, 682, 13, 216, 10, 7, 5473, 2889, 21, 915, 16, 30, 14, 23184, 12238, 34, 3876, 26, 127, 59, 25, 98209, 51841, 55, 16419, 42, 538, 250, 106, 11, 416020, 219602, 89, 69552, 68, 2279, 1059, 449, 18, 33 (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.  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).

Row 1 of R: A001076

Row 2 of R: A001077

Row 3 of R: A000045

Row 4 of R: A115179

Row 5 of R: A006355

Row 6 of R: A097924

Row 8 of R: A048875

Row 9 of R: A000032

LINKS

Table of n, a(n) for n=1..55.

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 (1,4,17,72,...).

_______________

Northwest corner of R:

   1   4   17   72  305  1292   5473

   2   9   38  161  682  2889  12238

   3   5    8   13   21    34     55

  12  51  216  915 3876 16419  69552

   6  10   16   26   42    68    110

   7  30  127  538 2279  9654  40895

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] == 0, 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]]

Table[u[n], {n, 1, 10}] (* A328695 array *)

v[n_, k_] := u[n][[k]];

Table[v[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A328695 sequence *)

CROSSREFS

Cf. A035513, A001076, A001077, A000045, A115179, A006355, A097924, A048875, A000032, A328696, A328697.

Sequence in context: A122749 A189741 A303142 * A285595 A255566 A302461

Adjacent sequences:  A328692 A328693 A328694 * A328696 A328697 A328698

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Oct 26 2019

STATUS

approved

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Last modified June 23 17:11 EDT 2021. Contains 345402 sequences. (Running on oeis4.)