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Triangle T(n,k) = 2*A046854(n,k) - 1, read by rows.
3

%I #10 Feb 18 2022 22:33:58

%S 1,1,1,1,1,1,1,3,1,1,1,3,5,1,1,1,5,5,7,1,1,1,5,11,7,9,1,1,1,7,11,19,9,

%T 11,1,1,1,7,19,19,29,11,13,1,1,1,9,19,39,29,41,13,15,1,1,1,9,29,39,69,

%U 41,55,15,17,1,1,1,11,29,69,69,111,55,71,17,19,1,1

%N Triangle T(n,k) = 2*A046854(n,k) - 1, read by rows.

%C Row sums = A131269: {1, 2, 3, 6, 11, 20, 35, 60, 101, 168, ...}.

%H G. C. Greubel, <a href="/A131270/b131270.txt">Rows n = 0..100 of triangle, flattened</a>

%F T(n,k) = 2*A046854(n,k) - 1.

%F Reversed triangle of A131268.

%e First few rows of the triangle:

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 3, 1, 1;

%e 1, 3, 5, 1, 1;

%e 1, 5, 5, 7, 1, 1;

%e 1, 5, 11, 7, 9, 1, 1;

%e 1, 7, 11, 19, 9, 11, 1, 1;

%e ...

%t Table[2*Binomial[Floor[(n+k)/2], k] - 1, {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jul 09 2019 *)

%o (PARI) T(n,k) = 2*binomial((n+k)\2, k)-1; \\ _G. C. Greubel_, Jul 09 2019

%o (Magma) [[2*Binomial(Floor((n+k)/2), k) -1: k in [0..n]]:n in [0..12]]; // _G. C. Greubel_, Jul 09 2019

%o (Sage) [[2*binomial(floor((n+k)/2), k) -1 for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Jul 09 2019

%Y Cf. A046854, A065941, A000012, A131268, A131269.

%K nonn,tabl

%O 0,8

%A _Gary W. Adamson_, Jun 23 2007