A062001 Table by antidiagonals of n-Stohr sequences: T(n,k) is least positive integer not the sum of at most n distinct terms in the n-th row from T(n,1) through to T(n,k-1).

1, 2, 1, 3, 2, 1, 4, 4, 2, 1, 5, 7, 4, 2, 1, 6, 10, 8, 4, 2, 1, 7, 13, 15, 8, 4, 2, 1, 8, 16, 22, 16, 8, 4, 2, 1, 9, 19, 29, 31, 16, 8, 4, 2, 1, 10, 22, 36, 46, 32, 16, 8, 4, 2, 1, 11, 25, 43, 61, 63, 32, 16, 8, 4, 2, 1, 12, 28, 50, 76, 94, 64, 32, 16, 8, 4, 2, 1, 13, 31, 57, 91, 125, 127, 64, 32, 16, 8, 4, 2, 1

Offset: 1

Author

Henry Bottomley, May 29 2001

Keywords

• nonn
• tabl

Examples

			Array begins as:
  1, 2, 3, 4,  5,  6,  7,   8,   9, ... A000027;
  1, 2, 4, 7, 10, 13, 16,  19,  22, ... A033627;
  1, 2, 4, 8, 15, 22, 29,  36,  43, ... A026474;
  1, 2, 4, 8, 16, 31, 46,  61,  76, ... A051039;
  1, 2, 4, 8, 16, 32, 63,  94, 125, ... A051040;
  1, 2, 4, 8, 16, 32, 64, 127, 190, ... ;
  1, 2, 4, 8, 16, 32, 64, 128, 255, ... ;
  1, 2, 4, 8, 16, 32, 64, 128, 256, ... ;
  1, 2, 4, 8, 16, 32, 64, 128, 256, ... ;
Antidiagonal triangle begins as:
   1;
   2,  1;
   3,  2,  1;
   4,  4,  2,  1;
   5,  7,  4,  2,   1;
   6, 10,  8,  4,   2,   1;
   7, 13, 15,  8,   4,   2,  1;
   8, 16, 22, 16,   8,   4,  2,  1;
   9, 19, 29, 31,  16,   8,  4,  2,  1;
  10, 22, 36, 46,  32,  16,  8,  4,  2, 1;
  11, 25, 43, 61,  63,  32, 16,  8,  4, 2, 1;
  12, 28, 50, 76,  94,  64, 32, 16,  8, 4, 2, 1;
  13, 31, 57, 91, 125, 127, 64, 32, 16, 8, 4, 2, 1;
		

Links

• G. C. Greubel, Antidiagonals n = 1..50, flattened

Crossrefs

Rows include A000027, A033627, A026474, A051039, A051040.

Diagonals include A000079, A000225, A033484, A036563, A048487.

Cf. A048488, A048489, A048490, A048491, A139634, A139635, A139697.

A048483 can be seen as half this table.

Programs

Mathematica

T[n_, k_]:= If[kG. C. Greubel, May 03 2022 *)

SageMath

def A062001(n,k):
    if (kA062001(n,k) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, May 03 2022

Formula

If k <= n+1 then A(n, k) = 2^(k-1), while if k > n+1, A(n, k) = (2^n - 1)*(k - n) + 1 (array).

T(n, k) = A(k, n-k+1) (antidiagonals).

T(2*n-1, n) = A000079(n-1), n >= 1.

T(2*n, n) = A000079(n), n >= 1.

T(2*n+1, n) = A000225(n+1), n >= 1.

T(2*n+2, n) = A033484(n), n >= 1.

T(2*n+3, n) = A036563(n+3), n >= 1.

T(2*n+4, n) = A048487(n), n >= 1.

From G. C. Greubel, May 03 2022: (Start)

T(n, k) = (2^k - 1)*(n-2*k+1) + 1 for k < n/2, otherwise 2^(n-k).

T(2*n+5, n) = A048488(n), n >= 1.

T(2*n+6, n) = A048489(n), n >= 1.

T(2*n+7, n) = A048490(n), n >= 1.

T(2*n+8, n) = A048491(n), n >= 1.

T(2*n+9, n) = A139634(n), n >= 1.

T(2*n+10, n) = A139635(n), n >= 1.

T(2*n+11, n) = A139697(n), n >= 1. (End)