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A332667 Permutation of N = {0, 1, 2, ...} induced by the enumeration of N X N in A332662. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

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], ...

...

MAPLE

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);

CROSSREFS

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

Sequence in context: A210863 A245816 A118461 * A266408 A230564 A011174

Adjacent sequences:  A332664 A332665 A332666 * A332668 A332669 A332670

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Feb 19 2020

STATUS

approved

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Last modified October 23 04:06 EDT 2021. Contains 348211 sequences. (Running on oeis4.)