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

Author

Rémy Sigrist, Jul 06 2024

Keywords

• nonn
• base
• tabf

Comments

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

Examples

			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
		

Links

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

Crossrefs

See A374354 for a similar sequence.

Cf. A005836, A120880, A374362, A374363.

Programs

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); }

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).