This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A375492 #11 Aug 18 2024 20:18:42 %S A375492 1,1,2,2,5,5,10,10,26,26,52,52,130,130,260,260,677,677,1354,1354,3385, %T A375492 3385,6770,6770,17602,17602,35204,35204,88010,88010,176020,176020, %U A375492 458330,458330,916660,916660,2291650,2291650,4583300,4583300,11916580,11916580 %N A375492 Number of compositions of n into powers of two that each divide the sum of previous powers. %C A375492 If n = 2^k, a(n) = A003095(k). Otherwise, a(n) is the product of terms from A003095 corresponding to the powers of two in the binary representation of n. If n is odd, the final term of the composition must be 1, so a(n) = a(n-1). %C A375492 Pieter Mostert points out that, after the first two values, this is a subsequence of A000404 (sums of two nonzero squares), because each term is either a square + 1 or a product of two earlier terms. %F A375492 Let p be the largest power of two less than n; then a(n) = a(p)a(n-p) if n is not a power of two, or a(n) = a(p)^2 + 1 if n is a power of two. %e A375492 For n = 4 the a(4) = 5 compositions are 1+1+1+1, 1+1+2, 2+1+1, 2+2, and 4. The composition 1+2+1 is not allowed, because 2 does not divide the sum of previous terms. %Y A375492 Cf. A023359, A003095. %K A375492 nonn %O A375492 0,3 %A A375492 _David Eppstein_, Aug 17 2024