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%I #15 May 19 2023 04:54:33
%S 1,2,2,4,5,4,6,6,4,8,10,8,13,14,10,14,13,8,14,16,12,18,18,12,16,14,8,
%T 16,20,16,26,28,20,28,26,16,29,34,26,40,41,28,38,34,20,34,38,28,41,40,
%U 26,34,29,16,30,36,28,44,46,32,44,40,24,42,48,36,54,54,36,48,42,24
%N Row sums of antidiagonals of the Sierpinski carpet A153490.
%C Also, sums of digits of terms of A292688, or Hamming weights of terms of A292689. See there or A153490 for definition / construction of the Sierpiski carpet.
%H Rémy Sigrist, <a href="/A293974/b293974.txt">Table of n, a(n) for n = 1..19683</a>
%F a(n) = A007953(A292688(n)) = A000120(A292689(n)) = sum(k=1..n, A153490(n,k)), considering A153490 as triangle; could also be indexed as matrix (m,n = 1,...,oo) or "flattened" (linearized) using A000217.
%t A293974[i_]:=With[{a=Nest[ArrayFlatten[{{#,#,#},{#,0,#},{#,#,#}}]&,{{1}},i]},Array[Total[Diagonal[a,#]]&,3^i,1-3^i]];A293974[5] (* Generates 3^5 terms *) (* _Paolo Xausa_, May 14 2023 *)
%o (PARI) A293974(n,A=Mat(1))={while(#A<n,A=matrix(3*#A,3*#A,i,j,if(A[(i+2)\3,(j+2)\3],i%3!=2||j%3!=2)));sum(k=1,n,A[k,n-k+1])}
%Y Cf. A153490, A292688, A292689, A000120, A007953, A000217.
%K nonn,look
%O 1,2
%A _M. F. Hasler_, Oct 24 2017
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