A135087 - OEIS

%I #13 Apr 25 2024 09:15:37

%S 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 3,3,27,83,139,139,83,27,3,3,31,111,223,279,223,111,31,3,3,35,143,335,

%U 503,503,335,143,35,3

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

%H G. C. Greubel, <a href="/A135087/b135087.txt">Rows n = 0..50 of the triangle, flattened</a>

%F T(n, k) = 2*A134058(n, k) - 1.

%F From _G. C. Greubel_, May 03 2021: (Start)

%F T(n, k) = 4*binomial(n, k) - 2*[n=0] - 1.

%F Sum_{k=0..n} T(n, k) = 2^(n+2) - (n + 1 + 2*[n=0]) = A095768(n) - 2*[n=0]. (End)

%e First few rows of the triangle are:

%e   1;

%e   3,  3;

%e   3,  7,  3;

%e   3, 11, 11,  3;

%e   3, 15, 23, 15,  3;

%e   3, 19, 39, 39, 19,  3;

%e   3, 23, 59, 79, 59, 23, 3;

%e   ...

%t Table[4*Binomial[n, k] -2*Boole[n==0] -1, {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, May 03 2021 *)

%o (Magma) [1] cat [4*Binomial(n,k) -1: k in [0..n], n in [1..12]]; // _G. C. Greubel_, May 03 2021

%o (Sage)

%o def A135087(n,k): return 4*binomial(n,k) -2*bool(n==0) -1

%o flatten([[A135087(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, May 03 2021

%Y Cf. A095768, A134058.

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Nov 18 2007