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 A157897 Triangle read by rows, T(n,k) = T(n-1,k) + T(n-2,k-1) + T(n-3,k-3) + delta(n,0)*delta(k,0), T(n,k<0) = T(n
 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 3, 1, 2, 0, 1, 4, 3, 3, 2, 0, 1, 5, 6, 5, 6, 0, 1, 1, 6, 10, 9, 12, 3, 3, 0, 1, 7, 15, 16, 21, 12, 6, 3, 0, 1, 8, 21, 27, 35, 30, 14, 12, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Sum of n-th row = A000073(n+2). - Reinhard Zumkeller, Jun 25 2009 T(n,k) is the number of tilings of an n-board that use k (1/2,1)-fences and n-k squares. A (1/2,1)-fence is a tile composed of two pieces of width 1/2 separated by a gap of width 1. (Result proved in paper by K. Edwards - see the links section.) - Michael A. Allen, Apr 28 2019 T(n,k) is the (n,n-k)-th entry in the (1/(1-x^3),x*(1+x)/(1-x^3)) Riordan array. - Michael A. Allen, Mar 11 2021 LINKS K. Edwards, A Pascal-like triangle related to the tribonacci numbers, Fib. Q., 46/47 (2008/2009), 18-25. 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, J. Int. Seq. 24 (2021) Article 21.3.8. FORMULA T(n,k) = T(n-1,k) + T(n-2,k-1) + T(n-3,k-3) + delta(n,0)*delta(k,0), T(n,k<0) = T(n

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Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)