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A131376 Triangle read by rows: T(n,k) = A007318(n,k) + A065941(n,k) - A168561(n,k).

%I A131376 #24 May 31 2025 09:42:23
%S A131376 1,2,1,1,3,1,2,2,5,1,1,5,6,6,1,2,3,14,9,8,1,1,7,14,24,16,9,1,2,4,27,
%T A131376 30,45,21,11,1,1,9,25,62,70,66,31,12,1,2,5,44,71,147,120,104,38,14,1,
%U A131376 1,11,39,128,203,273,217,140,51,15,1,2,6,65,139,366,434,518,329,200,60,17,1
%N A131376 Triangle read by rows: T(n,k) = A007318(n,k) + A065941(n,k) - A168561(n,k).
%C A131376 The old definition was: A007318 + A065941 - A049310. - _N. J. A. Sloane_, Aug 09 2019
%C A131376 Row sums = A117591: (1, 3, 5, 10, 19, 37, 72, ...).
%e A131376 First few rows of the triangle are:
%e A131376   1;
%e A131376   2, 1;
%e A131376   1, 3, 1;
%e A131376   2, 2, 5, 1;
%e A131376   1, 5, 6, 6, 1;
%e A131376   2, 3, 14, 9, 8, 1;
%e A131376   1, 7, 14, 24, 16, 9, 1;
%e A131376   ...
%t A131376 Table[Binomial[n, k] + Binomial[n - Floor[(k+1)/2], Floor[k/2]] - If[EvenQ[n+k], Binomial[(n+k)/2, k], 0], {n, 0, 11}, {k, 0, n}] // Flatten  (* _Amiram Eldar_, May 31 2025 *)
%Y A131376 Cf. A007318, A065941, A049310, A117591 (row sums), A131375, A168561, A309213.
%K A131376 nonn,tabl,easy
%O A131376 0,2
%A A131376 _Gary W. Adamson_, Jul 04 2007
%E A131376 The old definition of A131376 did not match its data, as _Michel Marcus_ pointed out. The definition has been corrected here, keeping the data. The old definition with corrected data is now A309213. - _N. J. A. Sloane_, Aug 09 2019
%E A131376 More terms from _Amiram Eldar_, May 31 2025