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 A334596 Number of values in A334556 with binary length n. 6
 2, 0, 0, 2, 0, 2, 4, 2, 0, 8, 4, 8, 16, 8, 16, 32, 0, 32, 64, 32, 64, 128, 64, 128, 256, 128, 256, 512, 256, 512, 1024, 512, 0, 2048, 1024, 2048, 4096, 2048, 4096, 8192, 4096, 8192, 16384, 8192, 16384, 32768, 16384, 32768, 65536, 32768, 65536, 131072, 65536, 131072, 262144, 131072 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All nonzero values are powers of two. LINKS Peter Kagey, Table of n, a(n) for n = 1..1024 MathOverflow user DSM, Number triangle Index entries for sequences related to binary expansion of n FORMULA Conjectured formula: a(1) = 2, a(n) = 0 if n = 2^k + 1 for some k, and a(n) = 2^A008611(n-4) otherwise. EXAMPLE For n = 11, the a(11) = 4 XOR-triangles of side length 11 are: 1 0 1 0 1 1 0 0 0 1 1, 1 0 1 1 1 0 0 1 0 1 1, 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 and their reflections across a vertical line. By reading the first rows in binary, these XOR-triangles correspond to A334556(20) = 1379, A334556(21) = 1483, A334556(22) = 1589, and A334556(23) = 1693 respectively. MATHEMATICA coeff[i_, j_, n_] := Binomial[i, j] - If[j + i == n, 1, 0]; A334596[1] = 2; A334596[n_] := ( nullsp = NullSpace[ Table[coeff[i, j, n - 1], {i, 0, n - 1}, {j, 0, n - 1}], Modulus -> 2]; If[AnyTrue[nullsp, #[[1]] == 1 &], 2^(Length[nullsp] - 1), 0] ); CROSSREFS Cf. A008611, A334556, A334591, A334592, A334593, A334594, A334595. Sequence in context: A262938 A143068 A261202 * A291900 A263146 A365047 Adjacent sequences: A334593 A334594 A334595 * A334597 A334598 A334599 KEYWORD nonn,base AUTHOR Peter Kagey, May 07 2020 EXTENSIONS More terms from Rémy Sigrist, May 08 2020 STATUS approved

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Last modified February 28 05:20 EST 2024. Contains 370379 sequences. (Running on oeis4.)