A293974 Row sums of antidiagonals of the Sierpinski carpet A153490.

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, 16, 20, 16, 26, 28, 20, 28, 26, 16, 29, 34, 26, 40, 41, 28, 38, 34, 20, 34, 38, 28, 41, 40, 26, 34, 29, 16, 30, 36, 28, 44, 46, 32, 44, 40, 24, 42, 48, 36, 54, 54, 36, 48, 42, 24

Offset: 1

Author

M. F. Hasler, Oct 24 2017

Keywords

• nonn
• look

Comments

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.

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..19683

Crossrefs

Cf. A153490, A292688, A292689, A000120, A007953, A000217.

Programs

Mathematica

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 *)

PARI

A293974(n,A=Mat(1))={while(#A
				

Formula

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.