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

1,2

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

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.

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 *)

Prog

(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])}

Crossrefs

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

Sequence in context: A332995 A214793 A199088 * A346036 A138557 A129303

Adjacent sequences: A293971 A293972 A293973 * A293975 A293976 A293977

Keyword

nonn,look

Author

M. F. Hasler, Oct 24 2017

Status

approved