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 A350532 #16 Jan 09 2022 23:50:20 %S A350532 1,0,0,1,1,0,1,0,0,1,1,2,1,0,0,1,0,0,1,0,0,1,3,3,2,1,0,0,1,0,0,0,0,0, %T A350532 0,1,1,4,6,4,1,0,0,0,0,1,0,0,4,1,0,2,0,0,0,1,5,10,11,5,1,0,0,1,0,0 %N A350532 Triangle read by rows: T(n,k) is the number of degree-n polynomials over Z/2Z of the form f(x)^m for some m > 1 with exactly k nonzero terms; 1 <= k <= n + 1. %C A350532 For n >= 1, row sums are given by A152061. %C A350532 Conjecture: T(n,n+1) = 1 if and only if n is a Mersenne prime (A000668). %C A350532 Conjecture: T(2*n,2) = n. %C A350532 Conjecture: T(2*n,3) = (n^2 - n)/2 for n >= 1. %e A350532 n\k| 1 2 3 4 5 6 7 8 9 10 11 %e A350532 ---+---------------------------------- %e A350532 0 | 1 %e A350532 1 | 0, 0 %e A350532 2 | 1, 1, 0 %e A350532 3 | 1, 0, 0, 1 %e A350532 4 | 1, 2, 1, 0, 0 %e A350532 5 | 1, 0, 0, 1, 0, 0 %e A350532 6 | 1, 3, 3, 2, 1, 0, 0 %e A350532 7 | 1, 0, 0, 0, 0, 0, 0, 1 %e A350532 8 | 1, 4, 6, 4, 1, 0, 0, 0, 0 %e A350532 9 | 1, 0, 0, 4, 1, 0, 2, 0, 0, 0 %e A350532 10 | 1, 5, 10, 11, 5, 1, 0, 0, 1, 0, 0 %e A350532 The T(6,4) = 2 degree-6 polynomials over Z/2Z with k=4 nonzero terms are %e A350532 1 + x^2 + x^4 + x^6 = (1 + x^2)^3 = (1 + x + x^2 + x^3)^2, and %e A350532 x^3 + x^4 + x^5 + x^6 = (x + x^2)^3. %Y A350532 Cf. A000668, A152061. %K A350532 nonn,tabl %O A350532 0,12 %A A350532 _Peter Kagey_, Jan 03 2022