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A345889
Number of tilings of an n-cell circular array with rectangular tiles of any size, and where the number of possible colors of a tile is given by the smallest cell covered.
1
1, 4, 16, 76, 436, 2956, 23116, 204556, 2018956, 21977356, 261478156, 3374988556, 46964134156, 700801318156, 11162196262156, 189005910310156, 3390192763174156, 64212742967590156, 1280663747055910156, 26826134832910630156, 588826498721714470156
OFFSET
1,2
LINKS
Jonathan Beagley and Lara Pudwell, Colorful Tilings and Permutations, Journal of Integer Sequences, Vol. 24 (2021), Article 21.10.4.
FORMULA
a(n) = Sum_{k=2..n+1} k!/2.
a(n) = A054116(n+1)/2.
a(n) = a(n-1) + A001710(n+1).
a(n) = A014288(n+1) - 1 = A003422(n+2)/2 - 1. - Alois P. Heinz, Jun 28 2021
a(n) ~ n*n!/2. - Stefano Spezia, Jun 29 2021
MATHEMATICA
Accumulate@ Array[#!/2 &, 21, 2] (* Michael De Vlieger, Jun 28 2021 *)
PROG
(PARI) a(n) = sum(k=2, n+1, k!/2); \\ Michel Marcus, Jun 29 2021
CROSSREFS
Partial differences give A001710.
Sequence in context: A255906 A260949 A049426 * A057725 A196192 A367261
KEYWORD
nonn
AUTHOR
Lara Pudwell, Jun 28 2021
STATUS
approved