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2*A051731 - A054525 as infinite lower triangular matrices.
2

%I #13 Feb 26 2022 10:48:06

%S 1,3,1,3,0,1,2,3,0,1,3,0,0,0,1,1,3,3,0,0,1,3,0,0,0,0,0,1,2,2,0,3,0,0,

%T 0,1,2,0,3,0,0,0,0,0,1,1,3,0,0,3,0,0,0,0,1,3,0,0,0,0,0,0,0,0,0,1,2,1,

%U 2,3,0,3,0,0,0,0,0,1,3,0,0,0,0,0,0,0,0,0,0,0,1

%N 2*A051731 - A054525 as infinite lower triangular matrices.

%C Row sums = A131089.

%C A131090: (1, 3, 3, 2, 3, 1, 3, 2, 2, 1, ...) in every column interspersed with (k-1) zeros.

%e First few rows of the triangle:

%e 1;

%e 3, 1;

%e 3, 0, 1;

%e 2, 3, 0, 1;

%e 3, 0, 0, 0, 1;

%e 1, 3, 3, 0, 0, 1

%e 3, 0, 0, 0, 0, 0, 1;

%e 2, 2, 0, 3, 0, 0, 0, 1;

%e ...

%o (PARI) T(n,k) = 2*!(n%k) - if (!(n % k), moebius(n/k), 0);

%o row(n) = vector(n, k, T(n,k));

%o lista(nn) = for (n=1, nn, v = row(n); for (k=1, #v, print1(v[k], ", "))); \\ _Michel Marcus_, Feb 26 2022

%Y Cf. A129979 (left border), A131089 (row sums), A051731, A054525.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Jun 14 2007

%E More terms from _Michel Marcus_, Feb 26 2022