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 A335964 Triangle read by rows, T(n,k) = T(n-1,k) + T(n-3,k-1) + T(n-4,k-2) + delta(n,0)*delta(k,0), T(n<0,k) = T(n
 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 3, 2, 0, 0, 0, 1, 4, 4, 0, 0, 0, 0, 1, 5, 7, 2, 0, 0, 0, 0, 1, 6, 11, 6, 1, 0, 0, 0, 0, 1, 7, 16, 13, 3, 0, 0, 0, 0, 0, 1, 8, 22, 24, 9, 0, 0, 0, 0, 0, 0, 1, 9, 29, 40, 22, 3, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 COMMENTS T(n,k) is the number of tilings of an n-board (a board with dimensions n X 1) using k (1,1)-fence tiles and n-2k square tiles. A (w,g)-fence tile is composed of two tiles of width w separated by a gap of width g. Sum of n-th row = A006498(n). LINKS Kenneth Edwards and Michael A. Allen, New Combinatorial Interpretations of the Fibonacci Numbers Squared, Golden Rectangle Numbers, and Jacobsthal Numbers Using Two Types of Tile, arXiv:2009.04649 [math.CO], 2020. FORMULA T(n,k) = A059259(n-k,k). T(n,2) = binomial(n-4,2) + n - 3. T(n,3) = binomial(n-6,3) + 2*binomial(n-5,2). EXAMPLE Triangle begins: 1; 1, 0; 1, 0, 0; 1, 1, 0, 0; 1, 2, 1, 0, 0; 1, 3, 2, 0, 0, 0; 1, 4, 4, 0, 0, 0, 0; 1, 5, 7, 2, 0, 0, 0, 0; 1, 6, 11, 6, 1, 0, 0, 0, 0; 1, 7, 16, 13, 3, 0, 0, 0, 0, 0; 1, 8, 22, 24, 9, 0, 0, 0, 0, 0, 0; 1, 9, 29, 40, 22, 3, 0, 0, 0, 0, 0, 0; ... MATHEMATICA T[n_, k_]:=If[n

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Last modified June 22 16:01 EDT 2021. Contains 345386 sequences. (Running on oeis4.)