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 A275204 Triangle read by rows: T(n,k) = number of domino stacks with n dominoes having a base of k dominoes. 3
 1, 1, 1, 1, 3, 1, 1, 4, 5, 1, 1, 6, 8, 7, 1, 1, 7, 15, 12, 9, 1, 1, 9, 22, 25, 16, 11, 1, 1, 10, 31, 43, 35, 20, 13, 1, 1, 12, 41, 68, 65, 45, 24, 15, 1, 1, 13, 54, 99, 113, 87, 55, 28, 17, 1, 1, 15, 66, 143, 178, 159, 109, 65, 32, 19, 1, 1, 16, 82, 193, 273, 267, 205, 131, 75, 36, 21, 1, 1, 18, 98, 258, 398, 430, 357, 251, 153, 85, 40, 23, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS The k-th column is the number of domino stacks having a base of k dominoes. The n-th row is the number of domino stacks consisting of n dominoes. A domino stack corresponds to a convex polyomino built with dominoes such that all columns intersect the base. LINKS Alois P. Heinz, Rows n = 1..200, flattened T. M. Brown Convex Domino Towers, J. Integer Seq. 20 (2017). FORMULA T(n,k) = Sum_{i=1..k} (2*(k-i)+1)*T(n-k,i) where T(n,n)=1 and T(n,k)=0 if n or k is nonpositive or if n is less than k. G.f.: x^k/(1-x^k) Sum_{S} (Product_{i=1..j} (2*(k_{i+1}-k_i)+1)*x^(k_i)/ (1-x^(k_i))) where the sum is over all subsets S of {1,..,k-1} such that S={k_1n, 0,       `if`(n=k, 1, add((2*(k-i)+1)*T(n-k, i), i=1..k)))     end: seq(seq(T(n, k), k=1..n), n=1..15);  # Alois P. Heinz, Jul 19 2016 MATHEMATICA T[n_, n_] = 1; T[n_, k_] /; n<1 || k<1 || n

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Last modified May 28 01:48 EDT 2020. Contains 334671 sequences. (Running on oeis4.)