Odd-side fills

• 2026-08-30 [Proved] At odd side n = 2k - 1 the residue split of an axis has k low positions and k - 1 high, so a base-2 flat design fills sum over its corners of k^(zeros) (k - 1)^(ones), and the six designs of the plane read as the polygonal numbers in k: low corner k^2 (A000290), tree k(2k - 1) hexagonal (A000384), carpet k(3k - 2) octagonal (A000567), void 2k^2 - 2k + 1 centered square (A001844), corner and centre 3k^2 - 3k + 1 centered hexagonal (A003215), solid (2k - 1)^2 odd squares (A016754); two_census at sides 3 to 11 returns 8, 21, 40, 65, 96 for the carpet and 6, 15, 28, 45, 66 for the tree. Witness: mrlymath::formulas::counting fill polynomial, mrlydemo two_census, A000567, A000384.