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%I A082222 #21 Feb 26 2021 02:32:52
%S A082222 1,2,2,4,7,10,12,14,17,18,21,26,30,34,40,45,51,55,62,66,72,74,82,89,
%T A082222 98,104,112,122,134,143,153,160,170,183,193,200,214,227,242,251,264,
%U A082222 275,287,298,312,327,342,359,372,384,399,411,429,444,463,477,485,502,510
%N A082222 a(n) = (n-th partial sum of A082219)/n = (n-th partial sum of the first row of array A082218)/n.
%e A082222 From _Petros Hadjicostas_, Feb 25 2021: (Start)
%e A082222 a(1) = A082219(1)/1 = 1/1 = 1.
%e A082222 a(2) = (A082219(1) + A082219(2))/2 = (1 + 3)/2 = 2.
%e A082222 a(3) = (A082219(1) + A082219(2) + A082219(3)) = (1 + 3 + 2)/3 = 2.
%e A082222 a(4) = (A082219(1) + ... + A082219(4))/4 = (1 + 3 + 2 + 10)/4 = 4. (End)
%o A082222 (PARI) lista(nn) = { my(a=matrix(nn, nn)); my(b=vector(nn)); my(d=vector(nn)); S=Set(); for(s=2, nn+1, if(s%2, i0=1; i1=s-1; i2=1, i0=s-1; i1=1; i2=-1);
%o A082222 forstep(i=i0, i1, i2, j=s-i; ii=sum(k=1, j-1, a[i, k]); jj=sum(k=1, i-1, a[k, j]);
%o A082222 c=chinese(Mod(ii, j), Mod(jj, i));
%o A082222 t=component(c, 1)-lift(c); while(setsearch(S, t), t+=component(c, 1));
%o A082222 a[i, j]=t; S=setunion(S, [t]); b[j] = sum(k=1, j, a[1, j])/j);); d[1]=b[1]; for(kk=1, nn, d[kk]=sum(ss=1,kk,b[ss])/kk); d;} \\ This is a modification of _Max Alekseyev_'s PARI program from A082219.
%Y A082222 Cf. A082218, A082219, A082220, A082221, A082223.
%K A082222 nonn
%O A082222 1,2
%A A082222 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 09 2003
%E A082222 More terms from _Max Alekseyev_, Jun 08 2007
%E A082222 Edited by _N. J. A. Sloane_, Jun 11 2007
%E A082222 Name edited by _Petros Hadjicostas_, Feb 25 2021

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