A326820 - OEIS

A326820

Irregular triangle read by rows; for n >= 0, the n-th row corresponds to the elements of the set {(n-k) OR k, k = 0..n}, in ascending order (where OR denotes the bitwise OR operator).

0, 1, 1, 2, 3, 2, 3, 4, 3, 5, 3, 5, 6, 7, 4, 6, 7, 8, 5, 7, 9, 5, 6, 7, 9, 10, 7, 11, 6, 7, 10, 11, 12, 7, 11, 13, 7, 11, 13, 14, 15, 8, 12, 14, 15, 16, 9, 13, 15, 17, 9, 10, 13, 14, 15, 17, 18, 11, 15, 19, 10, 11, 12, 14, 15, 18, 19, 20, 11, 13, 15, 19, 21

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OFFSET

0,4

COMMENTS

For any n >= 0, the n-th row:

- has sum A328566(n),

- has apparently length A002487(n+1),

- has last element n.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..9851 (rows n = 0..512)

EXAMPLE

Table begins:

1, 2;

2, 3, 4;

3, 5;

3, 5, 6;

4, 6, 7, 8;

5, 7, 9;

5, 6, 7, 9, 10;

7, 11;

6, 7, 10, 11, 12;

7, 11, 13;

7, 11, 13, 14;

...

MAPLE

T:= n-> sort([{seq(Bits[Or](n-k, k), k=0..n)}[]])[]:

seq(T(n), n=0..30); # Alois P. Heinz, Oct 20 2019

PROG

(PARI) row(n) = Set(apply(k -> bitor(n-k, k), [0..n]))

CROSSREFS

Cf. A326819 (AND variant), A328568 (XOR variant).

Cf. A002487, A328566.

Sequence in context: A194960 A111439 A020986 * A095161 A072106 A124524

Adjacent sequences: A326817 A326818 A326819 * A326821 A326822 A326823

KEYWORD

nonn,tabf,look,base

AUTHOR

Rémy Sigrist, Oct 20 2019

STATUS

approved