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A128622 Triangle T(n, k) = A128064(unsigned) * A128174, read by rows.

%I A128622 #7 Mar 14 2024 16:39:36
%S A128622 1,1,2,3,2,3,3,4,3,4,5,4,5,4,5,5,6,5,6,5,6,7,6,7,6,7,6,7,7,8,7,8,7,8,
%T A128622 7,8,9,8,9,8,9,8,9,8,9,9,10,9,10,9,10,9,10,9,10,11,10,11,10,11,10,11,
%U A128622 10,11,10,11,11,12,11,12,11,12,11,12,11,12,11,12
%N A128622 Triangle T(n, k) = A128064(unsigned) * A128174, read by rows.
%H A128622 G. C. Greubel, <a href="/A128622/b128622.txt">Rows n = 1..100 of the triangle, flattened</a>
%F A128622 T(n, k) = abs(A128064(n,k) * A128174(n, k), as infinite lower triangular matrices.
%F A128622 Sum_{k=1..n} T(n, k) = A014848(n) (row sums).
%F A128622 From _G. C. Greubel_, Mar 14 2024: (Start)
%F A128622 T(n, k) = n - (1 - (-1)^(n+k))/2 = n - (n+k mod 2).
%F A128622 T(n, 1) = A109613(n+1).
%F A128622 T(n, n) = A000027(n).
%F A128622 T(2*n-1, n) = A042963(n).
%F A128622 T(3*n-1, n) = A016777(n+1).
%F A128622 T(4*n-3, n) = A047461(n).
%F A128622 Sum_{k=1..n} (-1)^(k-1)*T(n, k) = A319556(n).
%F A128622 Sum_{k=1..floor((n+1)/2)} T(n-k+1, k) = A000326(floor((n+1)/2)).
%F A128622 Sum_{k=1..floor((n+1)/2)} (-1)^(k-1)*T(n-k+1, k) = A123684(floor((n+1)/2)). (End)
%e A128622 First few rows of the triangle are:
%e A128622   1;
%e A128622   1, 2;
%e A128622   3, 2, 3;
%e A128622   3, 4, 3, 4;
%e A128622   5, 4, 5, 4, 5;
%e A128622   5, 6, 5, 6, 5, 6;
%e A128622   7, 6, 7, 6, 7, 6, 7;
%e A128622   ...
%t A128622 Table[n - Mod[n+k,2], {n,16}, {k,n}]//Flatten (* _G. C. Greubel_, Mar 14 2024 *)
%o A128622 (Magma) [n - ((n+k) mod 2): k in [1..n], n in [1..16]]; // _G. C. Greubel_, Mar 14 2024
%o A128622 (SageMath) flatten([[n - ((n+k)%2) for k in range(1,n+1)] for n in range(1,16)]) # _G. C. Greubel_, Mar 14 2024
%Y A128622 Cf. A000027, A016777, A042963, A047461, A109613, A128064, A128174.
%Y A128622 Cf. A000326 (diagonal sums), A014848 (row sums), A319556 (alternating row sums).
%K A128622 nonn,tabl,easy
%O A128622 1,3
%A A128622 _Gary W. Adamson_, Mar 14 2007
%E A128622 More terms added by _G. C. Greubel_, Mar 14 2024