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A257564 Irregular triangle read by rows: T(n,k) = r(n+k)+r(n-k) with r(n) = (n-(n mod 2))/2 for n>=0 and -n<=k<=n.

%I A257564 #9 May 28 2015 07:13:52
%S A257564 0,1,0,1,2,1,2,1,2,3,2,3,2,3,2,3,4,3,4,3,4,3,4,3,4,5,4,5,4,5,4,5,4,5,
%T A257564 4,5,6,5,6,5,6,5,6,5,6,5,6,5,6,7,6,7,6,7,6,7,6,7,6,7,6,7,6,7,8,7,8,7,
%U A257564 8,7,8,7,8,7,8,7,8,7,8,7,8
%N A257564 Irregular triangle read by rows: T(n,k) = r(n+k)+r(n-k) with r(n) = (n-(n mod 2))/2 for n>=0 and -n<=k<=n.
%C A257564 r(n+k)-r(n-k) is triangle A196199(n,k).
%F A257564 Sum_{k=-n..n} T(n,k) = 2*n^2 = A001105(n).
%e A257564 Triangle starts:
%e A257564                  0;
%e A257564               1, 0, 1;
%e A257564            2, 1, 2, 1, 2;
%e A257564         3, 2, 3, 2, 3, 2, 3;
%e A257564      4, 3, 4, 3, 4, 3, 4, 3, 4;
%e A257564   5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5;
%p A257564 r := n -> (n-(n mod 2))/2: T := (n,k) -> r(n+k) + r(n-k):
%p A257564 seq(print(seq(T(n,k), k=-n..n)), n=0..6);
%o A257564 (Sage)
%o A257564 for n in (0..6):
%o A257564     [(n+k)//2 + (n-k)//2 for k in (-n..n)]
%Y A257564 Cf. A001105, A196199, A253580.
%K A257564 tabf,easy,nonn
%O A257564 0,5
%A A257564 _Peter Luschny_, May 28 2015