A342859 Table read by antidiagonals: T(n,k) = max(n,k) if n < 2 or k < 2; T(n,k) = T(n-1,k-1) + T(n-1,k-2) + T(n-2,k-1) otherwise.

0, 1, 1, 2, 1, 2, 3, 2, 2, 3, 4, 3, 3, 3, 4, 5, 4, 5, 5, 4, 5, 6, 5, 8, 7, 8, 5, 6, 7, 6, 11, 11, 11, 11, 6, 7, 8, 7, 14, 17, 17, 17, 14, 7, 8, 9, 8, 17, 24, 26, 26, 24, 17, 8, 9, 10, 9, 20, 31, 39, 39, 39, 31, 20, 9, 10, 11, 10, 23, 38, 55, 60, 60, 55, 38, 23, 10, 11

Offset

0,4

Links

Table of n, a(n) for n=0..77.

Example

  0,  1,  2,  3,  4,   5,   6,   7,    8,    9,    10,   11,   12
  1,  1,  2,  3,  4,   5,   6,   7,    8,    9,    10,   11,   12
  2,  2,  3,  5,  8,   11,  14,  17,   20,   23,   26,   29,   32
  3,  3,  5,  7,  11,  17,  24,  31,   38,   45,   52,   59,   66
  4,  4,  8,  11, 17,  26,  39,  55,   72,   89,   106,  123,  140
  5,  5,  11, 17, 26,  39,  60,  89,   125,  165,  206,  247,  288
  6,  6,  14, 24, 39,  60,  91,  138,  204,  286,  379,  477,  576
  7,  7,  17, 31, 55,  89,  138, 211,  318,  467,  655,  871,  1103
  8,  8,  20, 38, 72,  125, 204, 318,  487,  733,  1071, 1501, 2003
  9,  9,  23, 45, 89,  165, 286, 467,  733,  1123, 1687, 2459, 3443
  10, 10, 26, 52, 106, 206, 379, 655,  1071, 1687, 2589, 3881, 5647
  11, 11, 29, 59, 123, 247, 477, 871,  1501, 2459, 3881, 5963, 8929
  12, 12, 32, 66, 140, 288, 576, 1103, 2003, 3443, 5647, 8929, 13725

Mathematica

A[m_, n_]:= A[m, n] = Which[m < n, A[n, m], n < 2 || m < 2, Max[m, n], True,
  A[m-1, n-1] + A[m-1, n-2] + A[m-2, n-1]]; Table[A[k, n-k], {n, 0, 12}, {k, 0, n}] // Flatten

Prog

(PARI) A342859(n, k) = if(n<2||k<2, max(n, k), A342859(n-1, k-1)+A342859(n-1, k-2)+A342859(n-2, k-1)); \\ Antti Karttunen, Mar 28 2021

Crossrefs

Cf. A342600 (main diagonal).

Sequence in context: A344838 A344835 A082860 * A342385 A367108 A283845

Adjacent sequences: A342856 A342857 A342858 * A342860 A342861 A342862

Keyword

nonn,tabl

Author

José María Grau Ribas, Mar 26 2021

Status

approved