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%I #15 Aug 01 2023 07:51:01
%S 1,1,1,1,4,1,1,5,5,1,1,8,12,8,1,1,9,20,20,9,1,1,12,29,40,29,12,1,1,13,
%T 41,69,69,41,13,1,1,16,56,112,140,112,56,16,1,1,17,72,168,252,252,168,
%U 72,17,1,1,20,89,240,420,504,420,240,89,20,1,1,21,109,329,660,924,924,660,329,109,21,1
%N Triangle read by rows, twice Pascal's triangle minus Sierpinski's gasket: 2*A007318 - A047999.
%e First few rows of the triangle:
%e 1;
%e 1, 1;
%e 1, 4, 1;
%e 1, 5, 5, 1;
%e 1, 8, 12, 8, 1;
%e 1, 9, 20, 20, 9, 1;
%e 1, 12, 29, 40, 29, 12, 1;
%e 1, 13, 41, 69, 69, 41, 13, 1;
%e 1, 16, 56, 112, 140, 112, 56, 16, 1;
%e 1, 17, 72, 168, 252, 252, 168, 72, 17, 1;
%e 1, 20, 89, 240, 420, 504, 420, 240, 89, 20, 1;
%e 1, 21, 109, 329, 660, 924, 924, 660, 329, 109, 21, 1;
%e 1, 24, 132, 440, 989, 1584, 1848, 1584, 989, 440, 132, 24, 1;
%e ...
%t f[n_] := 2*n - Mod[n, 2]; T[n_, k_] := f[Binomial[n, k]]; Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Aug 01 2023 *)
%Y Cf. A007318, A047999, A166456 (row sums).
%K nonn,tabl
%O 0,5
%A _Gary W. Adamson_, Oct 14 2009
%E a(26) = 12 inserted and more terms from _Georg Fischer_, Jun 07 2023
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