OFFSET
1,2
COMMENTS
Row n is the ordered sequence of numbers k such that A118276(k) = n. As a sequence, A283938 is a permutation of the positive integers. As an array, A283938 is the joint-rank array (defined at A182801) of the numbers {i+j*r}, for i>=1, j>=1, where r = tau^2 = (3 + sqrt(5))/2. This is a transposable interspersion; i.e., every row intersperses all other rows, and every column intersperses all other columns.
LINKS
Clark Kimberling, Antidiagonals n = 1..60, flattened
Clark Kimberling and John E. Brown, Partial Complements and Transposable Dispersions, J. Integer Seqs., Vol. 7, 2004.
EXAMPLE
Northwest corner:
1 4 10 18 29 43 59 78 99 123
2 6 13 22 34 49 66 86 108 133
3 8 16 26 39 55 73 94 117 143
5 11 20 31 45 62 81 103 127 154
7 14 24 36 51 69 89 112 137 165
9 17 28 41 57 76 97 121 147 176
From Indranil Ghosh, Mar 19 2017: (Start)
Triangle formed when the array is read by antidiagonals:
1;
4, 2;
10, 6, 3;
18, 13, 8, 5;
29, 22, 16, 11, 7;
43, 34, 26, 20, 14, 9;
59, 49, 39, 31, 24, 17, 12;
78, 66, 55, 45, 36, 28, 21, 15;
99, 86, 73, 62, 51, 41, 33, 25, 19;
123, 108, 94, 81, 69, 57, 47, 38, 30, 23;
...
(End)
MATHEMATICA
PROG
(PARI)
\\ This code produces the triangle mentioned in the example section
r = (3 +sqrt(5))/2;
z = 100;
s(n) = if(n<1, 1, s(n - 1) + 1 + floor(n*r));
p(n) = n + 1 + sum(k=0, n, floor((n - k)/r));
u = v = vector(z + 1);
for(n=1, 101, (v[n] = s(n - 1)));
for(n=1, 101, (u[n] = p(n - 1)));
w(i, j) = v[i] + u[j] + (i - 1) * (j - 1) - 1;
tabl(nn) = {for(n=1, nn, for(k=1, n, print1(w(n - k + 1, k), ", "); ); print(); ); };
tabl(10) \\ Indranil Ghosh, Mar 19 2017
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Mar 18 2017
STATUS
approved