A126125 - OEIS

%I #9 Aug 12 2015 21:08:31

%S 1,2,1,5,2,1,11,7,2,1,27,15,9,2,1,61,44,19,11,2,1,149,97,65,23,13,2,1,

%T 342,267,141,90,27,15,2,1,835,599,433,193,119,31,17,2,1,1939,1598,956,

%U 655,253,152,35,19,2,1,4740,3631

%N Triangle equal to the matrix square of the triangle binomial(n,floor((n+1-(-1)^(n+k)*(k+1))/2)).

%C The triangular view of A061554 is:

%C 1;

%C 1, 1;

%C 2, 1, 1;

%C 3, 3, 1, 1;

%C 6, 4, 4, 1, 1;

%C The matrix square of this (infinite) triangle is this triangle here.

%e First few rows of the triangle are:

%e 1;

%e 2, 1;

%e 5, 2, 1;

%e 11, 7, 2, 1;

%e 27, 15, 9, 2, 1;

%e 61, 44, 19, 11, 2, 1;

%e ..,

%p A061554 := proc(n,k) local m ; m := floor((n+1)/2 - (-1)^(n-k)*(k+1)/2) ; binomial(n,m) ; end proc:

%p A126125 := proc(n,k) add(A061554(n,j)*A061554(j,k),j=k..n) ; end proc: # _R. J. Mathar_, Sep 17 2011

%Y Cf. A061554, A127358 (row sums).

%K tabl,easy,nonn

%O 0,2

%A _Gary W. Adamson_, Dec 17 2006