A131299 - OEIS

%I #25 Feb 24 2019 04:12:19

%S 1,1,1,1,1,1,1,1,4,1,1,1,7,4,1,1,1,10,7,7,1,1,1,13,10,16,7,1,1,1,16,

%T 13,28,16,10,1,1,1,19,16,43,28,28,10,1,1,1,22,19,61,43,58,28,13,1,1,1,

%U 25,22,82,61,103,58,43,13,1,1,1,28,25,106,82,166

%N Triangle T(n,k) = 3*binomial(n-floor((k+1)/2), floor(k/2))-2 with k=0..n, read by rows.

%C Row sums are in A131300. Reversed row triangle = A131301.

%C From _R. J. Mathar_, Apr 08 2013: (Start)

%C The matrix inverse starts

%C    1;

%C   -1,     1;

%C    0,    -1,       1;

%C    0,     3,      -4,     1;

%C    0,    -6,       9,    -4,      1;

%C    0,    30,     -45,    21,     -7,    1;

%C    0,  -132,     198,   -93,     33,   -7,    1;

%C    0,   984,   -1476,   693,   -246,   54,  -10,   1;

%C    0, -6756,   10134, -4758,   1689, -372,   72, -10,   1;

%C    0, 66972, -100458, 47166, -16743, 3687, -714, 102, -13, 1;

%C (End)

%H Nathaniel Johnston, <a href="/A131299/b131299.txt">Rows n = 0..100, flattened</a>

%F 3*A065941 - 2*A000012 as infinite lower triangular matrices.

%e Triangle begins:

%e   1;

%e   1,  1;

%e   1,  1,  1;

%e   1,  1,  4,  1;

%e   1,  1,  7,  4,  1;

%e   1,  1, 10,  7,  7,  1;

%e   1,  1, 13, 10, 16,  7,  1;

%e   ...

%p A131299 := proc(n,k) 3*binomial(n-floor((k+1)/2),floor(k/2))-2 ; end proc; # _Nathaniel Johnston_, Jun 30 2011

%Y Cf. A065941, A000012, A131300, A131301.

%K nonn,tabl,easy

%O 0,9

%A _Gary W. Adamson_, Jun 27 2007

%E Better definition from _Bruno Berselli_, May 03 2012