A250003 -id:A250003 - cp's OEIS frontend

A250002 Triangle read by rows: T(n,k) = number of inequivalent binary linear [n,k] codes minus C(n,k).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 8, 8, 2, 0, 0, 0, 0, 4, 21, 36, 21, 4, 0, 0, 0, 0, 7, 47, 114, 114, 47, 7, 0, 0, 0, 0, 11, 93, 306, 453, 306, 93, 11, 0, 0, 0, 0, 16, 168, 730, 1526, 1526, 730, 168, 16, 0, 0

Offset: 0

Tilman Piesk, Nov 10 2014

The triangle of inequivalent binary linear [n,k] codes (A076831) looks much like Pascal's triangle (A007318). They start to differ in the middle of row 6. This triangle is the difference between them. Its row sums are A250003 - the difference between the numbers of inequivalent binary linear codes of length n (A076766) and the powers of two (A000079).

			      k   0   1   2   3   4    5    6   7   8   9  10  11      sums
   n
   0      0                                                       0
   1      0   0                                                   0
   2      0   0   0                                               0
   3      0   0   0   0                                           0
   4      0   0   0   0   0                                       0
   5      0   0   0   0   0    0                                  0
   6      0   0   1   2   1    0    0                             4
   7      0   0   2   8   8    2    0   0                        20
   8      0   0   4  21  36   21    4   0   0                    86
   9      0   0   7  47 114  114   47   7   0   0               336
  10      0   0  11  93 306  453  306  93  11   0   0          1273
  11      0   0  16 168 730 1526 1526 730 168  16   0   0      4880
Row 6 of A076831 is (1,6,16,22,16,6,1) and row 6 of A007318 is (1,6,15,20,15,6,1). Row 6 of this triangle is their difference (0,0,1,2,1,0,0).

Cf. A076831, A007318, A250003.

a(n,k) = A076831(n,k) - A007318(n,k).

cp's OEIS Frontend

A250002 Triangle read by rows: T(n,k) = number of inequivalent binary linear [n,k] codes minus C(n,k).

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