A374361 Irregular table T(n, k), n >= 0, 0 <= k < A120880(n), read by rows; the n-th row contains the terms t of A005836 such that n - t also belongs to A005836.

0, 0, 1, 1, 0, 3, 0, 1, 3, 4, 1, 4, 3, 3, 4, 4, 0, 9, 0, 1, 9, 10, 1, 10, 0, 3, 9, 12, 0, 1, 3, 4, 9, 10, 12, 13, 1, 4, 10, 13, 3, 12, 3, 4, 12, 13, 4, 13, 9, 9, 10, 10, 9, 12, 9, 10, 12, 13, 10, 13, 12, 12, 13, 13, 0, 27, 0, 1, 27, 28, 1, 28, 0, 3, 27, 30, 0, 1, 3, 4, 27, 28, 30, 31

Offset

0,6

Comments

In other words, we partition n into pairs of terms of A005836 and list the corresponding terms to get the n-th row.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..4095 (rows for n = 0..3^6-1 flattened)

Formula

T(n, 0) = 0 iff n belongs to A005836.

T(n, k) + T(n, A120880(k)-1-k) = n.

T(n, 0) = A374362(n).

T(n, A120880(k)-1) = A374363(n).

Example

Triangle T(n, k) begins:
  n   n-th row
  --  -----------
   0  0
   1  0, 1
   2  1
   3  0, 3
   4  0, 1, 3, 4
   5  1, 4
   6  3
   7  3, 4
   8  4
   9  0, 9
  10  0, 1, 9, 10
  11  1, 10
  12  0, 3, 9, 12

Prog

(PARI) row(n) = { my (r = [0], t = 1, d); while (n, d = n % 3; n \= 3; if (d==1, r = concat(r, [v + t | v <- r]), d==2, r = [v + t | v <- r]); t *= 3; ); return (r); }

Crossrefs

See A374354 for a similar sequence.

Cf. A005836, A120880, A374362, A374363.

Sequence in context: A279010 A121481 A366875 * A121469 A091867 A127158

Adjacent sequences: A374358 A374359 A374360 * A374362 A374363 A374364

Keyword

nonn,base,tabf

Author

Rémy Sigrist, Jul 06 2024

Status

approved