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A126125 Triangle equal to the matrix square of the triangle binomial(n,floor((n+1-(-1)^(n+k)*(k+1))/2)).

%I A126125 #9 Aug 12 2015 21:08:31
%S A126125 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 A126125 342,267,141,90,27,15,2,1,835,599,433,193,119,31,17,2,1,1939,1598,956,
%U A126125 655,253,152,35,19,2,1,4740,3631
%N A126125 Triangle equal to the matrix square of the triangle binomial(n,floor((n+1-(-1)^(n+k)*(k+1))/2)).
%C A126125 The triangular view of A061554 is:
%C A126125 1;
%C A126125 1, 1;
%C A126125 2, 1, 1;
%C A126125 3, 3, 1, 1;
%C A126125 6, 4, 4, 1, 1;
%C A126125 The matrix square of this (infinite) triangle is this triangle here.
%e A126125 First few rows of the triangle are:
%e A126125 1;
%e A126125 2, 1;
%e A126125 5, 2, 1;
%e A126125 11, 7, 2, 1;
%e A126125 27, 15, 9, 2, 1;
%e A126125 61, 44, 19, 11, 2, 1;
%e A126125 ..,
%p A126125 A061554 := proc(n,k) local m ; m := floor((n+1)/2 - (-1)^(n-k)*(k+1)/2) ; binomial(n,m) ; end proc:
%p A126125 A126125 := proc(n,k) add(A061554(n,j)*A061554(j,k),j=k..n) ; end proc: # _R. J. Mathar_, Sep 17 2011
%Y A126125 Cf. A061554, A127358 (row sums).
%K A126125 tabl,easy,nonn
%O A126125 0,2
%A A126125 _Gary W. Adamson_, Dec 17 2006