A332699 -id:A332699 - cp's OEIS frontend

A332667 Permutation of N = {0, 1, 2, ...} induced by the enumeration of N X N in A332662.

0, 1, 2, 4, 5, 3, 10, 11, 6, 7, 20, 21, 12, 13, 8, 35, 36, 22, 23, 14, 9, 56, 57, 37, 38, 24, 15, 16, 84, 85, 58, 59, 39, 25, 26, 17, 120, 121, 86, 87, 60, 40, 41, 27, 18, 165, 166, 122, 123, 88, 61, 62, 42, 28, 19, 220, 221, 167, 168, 124, 89, 90, 63, 43, 29, 30

Offset: 0

Peter Luschny, Feb 19 2020

Motivated by the question how a sequence of regular integer triangles can be stored in linear memory (see A332662).

			a(n) can be seen as the triangle read by rows:
[0]  0;
[1]  1,  2;
[2]  4,  5,  3;
[3] 10, 11,  6,  7;
[4] 20, 21, 12, 13, 8;
[5] 35, 36, 22, 23, 14, 9;
[6] 56, 57, 37, 38, 24, 15, 16;
[7] 84, 85, 58, 59, 39, 25, 26, 17;
...
a(n) can also be seen as the rectangular array read by upwards antidiagonals (with flat rows):
(A) [ 0], [ 2,  3], [ 7,  8,  9], [16, 17, 18, 19], [30, 31, 32, 33, 34],...
(B) [ 1], [ 5,  6], [13, 14, 15], [26, 27, 28, 29], ...
(C) [ 4], [11, 12], [23, 24, 25], ...
(D) [10], [21, 22], ...
(E) [20], ...
...

Cf. A332662, A000292 (first column), A332699 (main diagonal).

F := L -> ListTools:-Flatten(L): b := n -> floor((sqrt(8*n+1)-1)/2):
S := (n, k) -> [seq(binomial(n+k+2,3) + binomial(k+1,2)+j, j=0..k)]:
A332667 := (n, k) -> F([seq(S(n-k,j), j=0..b(k))])[k+1]:
seq(seq(A332667(n, k), k=0..n), n=0..10);

cp's OEIS Frontend

A332667 Permutation of N = {0, 1, 2, ...} induced by the enumeration of N X N in A332662.

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