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A250002 Triangle read by rows: T(n,k) = number of inequivalent binary linear [n,k] codes minus C(n,k). 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,25

COMMENTS

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).

LINKS

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

FORMULA

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

EXAMPLE

      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).

CROSSREFS

Cf. A076831, A007318, A250003.

Sequence in context: A113448 A123863 A244560 * A035195 A073797 A037856

Adjacent sequences:  A249999 A250000 A250001 * A250003 A250004 A250005

KEYWORD

nonn,tabl

AUTHOR

Tilman Piesk, Nov 10 2014

STATUS

approved

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Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)