A131779 - OEIS

%I #5 Sep 08 2018 16:07:28

%S 1,3,1,1,3,1,3,1,5,1,1,3,5,5,1,3,1,9,5,7,1,1,3,9,9,11,7,1,3,1,13,9,21,

%T 11,9,1,1,3,13,13,29,21,19,9,1,3,1,17,13,43,29,41,19,11,1,1,3,17,17,

%U 55,43,69,41,29,11,1,3,1,21,17,73,55,113,69,71,29,13,1

%N Triangle read by rows: T(n,k) = 2*A065941(n-1,k-1) - (-1)^(n+k).

%H Andrew Howroyd, <a href="/A131779/b131779.txt">Table of n, a(n) for n = 1..1275</a> (first 50 rows)

%F T(n,k) = 2*binomial(n-1-floor(k/2), floor((k-1)/2)) - (-1)^(n+k). - _Andrew Howroyd_, Sep 08 2018

%e First few rows of the triangle are:

%e   1;

%e   3, 1;

%e   1, 3, 1;

%e   3, 1, 5, 1;

%e   1, 3, 5, 5, 1;

%e   3, 1, 9, 5, 7, 1;

%e   1, 3, 9, 9, 11, 7, 1;

%e   ...

%o (PARI) T(n,k) = {if(k<=n, 2*binomial(n-1-k\2, (k-1)\2) - (-1)^(n+k), 0)} \\ _Andrew Howroyd_, Sep 08 2018

%Y Row sums are A131780.

%Y Cf. A065941.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Jul 14 2007

%E a(28)-a(29) corrected and terms a(56) and beyond from _Andrew Howroyd_, Sep 08 2018