The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A251072 Number A(n,k) of tilings of a 3k X n rectangle using 3n k-ominoes of shape I; square array A(n,k), n>=0, k>=0, read by antidiagonals. 11
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 41, 1, 1, 1, 1, 1, 19, 281, 1, 1, 1, 1, 1, 1, 57, 1183, 1, 1, 1, 1, 1, 1, 26, 121, 6728, 1, 1, 1, 1, 1, 1, 1, 75, 783, 31529, 1, 1, 1, 1, 1, 1, 1, 34, 154, 2861, 167089, 1, 1, 1, 1, 1, 1, 1, 1, 95, 269, 8133, 817991, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS A(n,n) = A034856(n+2) for n>=2. LINKS Alois P. Heinz, Antidiagonals n = 0..35, flattened Wikipedia, Polyomino EXAMPLE Square array A(n,k) begins: 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 1, 13, 1, 1, 1, 1, 1, 1, ... 1, 1, 41, 19, 1, 1, 1, 1, 1, ... 1, 1, 281, 57, 26, 1, 1, 1, 1, ... 1, 1, 1183, 121, 75, 34, 1, 1, 1, ... 1, 1, 6728, 783, 154, 95, 43, 1, 1, ... 1, 1, 31529, 2861, 269, 190, 117, 53, 1, ... 1, 1, 167089, 8133, 1732, 325, 229, 141, 64, ... MAPLE b:= proc(n, l) option remember; local d, k; d:= nops(l)/3; if n=0 then 1 elif min(l[])>0 then (m->b(n-m, map(x->x-m, l)))(min(l[])) else for k while l[k]>0 do od; `if`(n2*d+1 or max(l[k..k+d-1][])>0, 0, b(n, [l[1..k-1][], 1\$d, l[k+d..3*d][]])) fi end: A:= (n, k)-> `if`(k=0, 1, b(n, [0\$3*k])): seq(seq(A(n, d-n), n=0..d), d=0..12); MATHEMATICA b[n_, l_List] := b[n, l] = Module[{d = Length[l]/3, k}, Which[n == 0, 1, Min[l] > 0, Function[{m}, b[n-m, l-m]][Min[l]], True, For[k=1, l[[k]] > 0 , k++]; If[n d]]] + If[d == 1 || k > 2d + 1 || Max[l[[k ;; k + d - 1]]] > 0, 0, b[n, Join[l[[1 ;; k-1]], Array[1&, d], l[[k+d ;; 3*d]]]]]]]; A[n_, k_] := If[k == 0, 1, b[n, Array[0&, 3k]]]; Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Jan 30 2015, after Alois P. Heinz *) CROSSREFS Columns k=0+1,2-10 give: A000012, A028468, A251073, A251074, A247218, A251075, A251076, A251077, A251078, A251079. Cf. A034856, A250662. Sequence in context: A165400 A181154 A357912 * A353805 A332018 A010227 Adjacent sequences: A251069 A251070 A251071 * A251073 A251074 A251075 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Nov 29 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 24 18:34 EDT 2023. Contains 361510 sequences. (Running on oeis4.)