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a(n) = (n-th partial sum of A082220)/n = (n-th partial sum of the first column of array A082218)/n.
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%I #18 Feb 26 2021 02:09:34

%S 1,3,4,4,5,6,8,13,15,19,20,26,28,34,38,45,49,57,62,71,78,85,92,101,

%T 109,117,129,137,143,152,161,168,175,185,196,207,218,230,238,246,257,

%U 269,281,294,309,322,331,347,357,371,385,397,413,432,451,468,484,504,518

%N a(n) = (n-th partial sum of A082220)/n = (n-th partial sum of the first column of array A082218)/n.

%o (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 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 c=chinese(Mod(ii, j), Mod(jj, i));

%o t=component(c, 1)-lift(c); while(setsearch(S, t), t+=component(c, 1));

%o a[i, j]=t; S=setunion(S, [t]); b[i] = a[i, 1];); ); 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. - _Petros Hadjicostas_, Feb 25 2021

%Y Cf. A082218, A082219, A082220, A082221, A082222.

%K nonn

%O 1,2

%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 09 2003

%E More terms from _Max Alekseyev_, Jun 08 2007

%E Edited by _N. J. A. Sloane_, Jun 11 2007

%E Name edited by _Petros Hadjicostas_, Feb 25 2021