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A135087 Triangle T(n, k) = 2*A134058(n, k) - 1, read by rows.

%I A135087 #13 Apr 25 2024 09:15:37
%S A135087 1,3,3,3,7,3,3,11,11,3,3,15,23,15,3,3,19,39,39,19,3,3,23,59,79,59,23,
%T A135087 3,3,27,83,139,139,83,27,3,3,31,111,223,279,223,111,31,3,3,35,143,335,
%U A135087 503,503,335,143,35,3
%N A135087 Triangle T(n, k) = 2*A134058(n, k) - 1, read by rows.
%H A135087 G. C. Greubel, <a href="/A135087/b135087.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A135087 T(n, k) = 2*A134058(n, k) - 1.
%F A135087 From _G. C. Greubel_, May 03 2021: (Start)
%F A135087 T(n, k) = 4*binomial(n, k) - 2*[n=0] - 1.
%F A135087 Sum_{k=0..n} T(n, k) = 2^(n+2) - (n + 1 + 2*[n=0]) = A095768(n) - 2*[n=0]. (End)
%e A135087 First few rows of the triangle are:
%e A135087   1;
%e A135087   3,  3;
%e A135087   3,  7,  3;
%e A135087   3, 11, 11,  3;
%e A135087   3, 15, 23, 15,  3;
%e A135087   3, 19, 39, 39, 19,  3;
%e A135087   3, 23, 59, 79, 59, 23, 3;
%e A135087   ...
%t A135087 Table[4*Binomial[n, k] -2*Boole[n==0] -1, {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, May 03 2021 *)
%o A135087 (Magma) [1] cat [4*Binomial(n,k) -1: k in [0..n], n in [1..12]]; // _G. C. Greubel_, May 03 2021
%o A135087 (Sage)
%o A135087 def A135087(n,k): return 4*binomial(n,k) -2*bool(n==0) -1
%o A135087 flatten([[A135087(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, May 03 2021
%Y A135087 Cf. A095768, A134058.
%K A135087 nonn,tabl
%O A135087 0,2
%A A135087 _Gary W. Adamson_, Nov 18 2007