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A128282 For definition see Comment lines . 1

%I

%S 1,2,2,3,4,3,5,6,6,5,7,8,9,8,7,10,11,12,12,11,10,13,14,15,16,15,14,13,

%T 17,18,19,20,20,19,18,17,21,22,23,24,25,24,23,22,21,26,27,28,29,30,30,

%U 29,28,27,26,31,32,33,34,35,36,35,34,33,32,31,37,38,39,40,41,42,42,41

%N For definition see Comment lines .

%C Left half triangle is A000027 (natural numbers): 1 ; 2 ; 3, 4 ; 5, 6 ; 7, 8, 9 ; 10, 11, 12 ; 13, 14, 15, 16 ; 17, 18, 19, 20 ;...

%F T(n,k) = T(n,n-k).

%F T(2*n,n) = (n+1)^2 = A000290(n+1).

%F T(n,0) = T(n,n) = A033638(n+1).

%F From _Yu-Sheng Chang_, May 25 2020: (Start)

%F O.g.f.: F(z,v) = (z/((-z+1)^3*(z+1))-v^2*z/((-v*z+1)^3*(v*z+1)))/(1-v)+1/((-z+1)*(-v*z+1)*(-v*z^2+1)).

%F T(n,k) = [v^k] (1/8)*(1-v^(n+1))*(2*(n+1)^2-1-(-1)^n)/(1-v) + (v^(2+n)+(1/2*((sqrt(v)-1)^2*(-1)^n-(sqrt(v)+1)^2))*v^((1/2)*n+1/2)+1)/(1-v)^2.

%F T(n,k) = 1 + (1/4)*n*(n+1) + min(k, n-k) + (1/2)*ceiling((1/2)*n). (End)

%e Triangle begins:

%e 1;

%e 2, 2;

%e 3, 4, 3;

%e 5, 6, 6, 5;

%e 7, 8, 9, 8, 7;

%e 10, 11, 12, 12, 11, 10;

%e 13, 14, 15, 16, 15, 14, 13;

%e 17, 18, 19, 20, 20, 19, 18, 17;

%e ...

%p A := proc(n,k) ## n >= 0 and k = 0 .. n

%p 1+(1/4)*n*(n+1)+min(k, n-k)+(1/2)*ceil((1/2)*n)

%p end proc: # _Yu-Sheng Chang_, May 25 2020

%Y Cf. A000027, A000290, A033638 (1st column and right diagonal).

%K nonn,tabl

%O 0,2

%A _Philippe Deléham_, May 03 2007

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Last modified May 13 05:02 EDT 2021. Contains 343836 sequences. (Running on oeis4.)