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 A306287 Irregular triangle T(n,k), 1 <= n, 1 <= k <= (1/6)*(4+5*2^(2*n)), read by rows: T(n,k) determines absolute directions along the perimeter of the n-th Y-type Hilbert Tree. 3
 1, 0, 3, 2, 1, 2, 1, 1, 0, 3, 0, 1, 0, 3, 3, 2, 3, 2, 1, 2, 1, 0, 1, 2, 2, 3, 2, 1, 1, 0, 1, 2, 1, 1, 0, 3, 0, 1, 0, 3, 3, 2, 3, 0, 0, 0, 1, 2, 1, 1, 0, 3, 0, 1, 0, 3, 3, 2, 3, 0, 3, 3, 2, 1, 2, 2, 3, 0, 3, 2, 3, 2, 1, 2, 1, 0, 1, 2, 2, 3, 2, 1, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The Y-type Hilbert trees are a sequence of polyominoes whose edges, all but one, are segments of the Hilbert curve described by A163540. One extra edge closes a loop around the perimeter (cf. Formula). The first Y-type tree is a monomino with four edges, and the second is the Y hexomino with 14 unit edges. All deeper trees are determined by iteration of replacement rules (cf. linked image "First Six Y-type Trees"). The Y-type Hilbert trees nest along the upper half plane according to the limit-periodic ruler function A001511. Such an arrangement reconstructs the Hilbert curve everywhere away from the ground axis (cf. linked image "Limit-Periodic Construction"). LINKS Table of n, a(n) for n=1..85. Bradley Klee, Limit-Periodic Construction. Bradley Klee, First Six Y-type Trees. FORMULA a(n,(1/6)*(4+5*2^(2*n))) = 2; a(n,k) = A163540( (1/12)*(8+7*2^(2*n)-3*(-1)^n *2^(2*n+1))-1+k ). EXAMPLE T(1,k) = 1, 0, 3, 2; T(2,k) = 1, 2, 1, 1, 0, 3, 0, 1, 0, 3, 3, 2, 3, 2. MATHEMATICA HC = {L[n_ /; EvenQ[n]] :> {F[n], L[n], L[Mod[n + 1, 2]], R[n]}, R[n_ /; OddQ[n]] :> {F[n], R[n], R[Mod[n + 1, 2]], L[n]}, R[n_ /; EvenQ[n]] :> {L[n], R[Mod[n + 1, 2]], R[n], F[Mod[n + 1, 2]]}, L[n_ /; OddQ[n]] :> {R[n], L[Mod[n + 1, 2]], L[n], F[Mod[n + 1, 2]]}, F[n_ /; EvenQ[n]] :> {L[n], R[Mod[n + 1, 2]], R[n], L[Mod[n + 1, 2]]}, F[n_ /; OddQ[n]] :> {R[n], L[Mod[n + 1, 2]], L[n], R[Mod[n + 1, 2]]}}; TurnMap = {F[_] -> 0, L[_] -> 1, R[_] -> -1}; T1ind[1] = 1; T1ind[2] = 2; T1ind[n_] := 5*T1ind[n - 1] - 4*T1ind[n - 2]; T1Vec[n_] := Append[Mod[FoldList[Plus, Flatten[Nest[# /. HC &, F[0], n] /. TurnMap][[T1ind[n] ;; -(T1ind[n] + 1)]]], 4], 2] Flatten[T1Vec /@ Range[5]] CROSSREFS T-Type Trees: A306288. Cf. A163540, A001511, A246559. Sequence in context: A245188 A137241 A331539 * A016457 A181715 A077089 Adjacent sequences: A306284 A306285 A306286 * A306288 A306289 A306290 KEYWORD tabf,nonn AUTHOR Bradley Klee, Feb 03 2019 STATUS approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)