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%I #14 Nov 28 2014 22:24:26
%S 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,
%T 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,
%U 306,93,11,0,0,0,0,16,168,730,1526,1526,730,168,16,0,0
%N Triangle read by rows: T(n,k) = number of inequivalent binary linear [n,k] codes minus C(n,k).
%C 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).
%F a(n,k) = A076831(n,k) - A007318(n,k).
%e k 0 1 2 3 4 5 6 7 8 9 10 11 sums
%e n
%e 0 0 0
%e 1 0 0 0
%e 2 0 0 0 0
%e 3 0 0 0 0 0
%e 4 0 0 0 0 0 0
%e 5 0 0 0 0 0 0 0
%e 6 0 0 1 2 1 0 0 4
%e 7 0 0 2 8 8 2 0 0 20
%e 8 0 0 4 21 36 21 4 0 0 86
%e 9 0 0 7 47 114 114 47 7 0 0 336
%e 10 0 0 11 93 306 453 306 93 11 0 0 1273
%e 11 0 0 16 168 730 1526 1526 730 168 16 0 0 4880
%e 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).
%Y Cf. A076831, A007318, A250003.
%K nonn,tabl
%O 0,25
%A _Tilman Piesk_, Nov 10 2014
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