Symmetric Odd Tree (Center = 3) — Pascal Multiplicities & Sierpiński Masks

Row n shows the ±2 walk of length n. Multiplicity of value 3+2k is C(n,(n+k)/2) when n+k is even.


Σ = 3·2^n, mean = 3, var = 4n


Legend (value mod m): 01 23 45 67 8

Row sum: ∑ (3+2k)·C(n,(n+k)/2) = 3·2ⁿ; Average = 3; Quadratic moment: ∑ (3+2k)²·C(n,(n+k)/2) = (9+4n)·2ⁿ.

Toggle “p = 2 (Sierpiński)” to see the classic odd/even binomial mask. Larger p (3,5,7) reveal Lucas-type modular patterns in Pascal’s triangle, transferred to your odd-walk lattice.

Original center-3 tree for reference: symmetric-odd-tree-center3.html