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 A329279 Number of distinct tilings of a 2n X 2n square with 1 x n polyominoes. 1
 1, 9, 11, 19, 22, 33, 37, 51, 56, 73, 79, 99, 106, 129, 137, 163, 172, 201, 211, 243, 254, 289, 301, 339, 352, 393, 407, 451, 466, 513, 529, 579, 596, 649, 667, 723, 742, 801, 821, 883, 904, 969, 991, 1059, 1082, 1153, 1177, 1251, 1276, 1353, 1379, 1459, 1486, 1569, 1597, 1683, 1712, 1801, 1831 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The positions of n X n subsquares greatly restricts which permutations are possible, simplifying finding solutions.  a(n+1) - a(n) = A014682 (n+2), where A014682 is the Collatz function, except a(2)-a(1) = 8 and A014682(4) = 5. LINKS Jeff Bowermaster, Illustration of a(1)..a(3) Jeff Bowermaster, Illustration of a(4) and a(5) Jeff Bowermaster, Illustration of a(6) Jeff Bowermaster, Illustration of a(7) Jeff Bowermaster, Illustration of a(8) FORMULA For even n, a(n) = (n^2+4n)/2+3; for odd n, a(n) = (n^2+3n)/2+2 ; a(1) = 1. PROG (Pari)  a(n) = if(n==1, 1, if(n%2, (n^2+3*n)/2+2, (n^2+4*n)/2+3)) CROSSREFS Cf. A014682, A060312, A058331 (bisection). Sequence in context: A263722 A299971 A090771 * A284295 A284294 A195572 Adjacent sequences:  A329276 A329277 A329278 * A329280 A329281 A329282 KEYWORD nonn AUTHOR Jeff Bowermaster, Nov 11 2019 STATUS approved

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Last modified January 26 01:48 EST 2020. Contains 331270 sequences. (Running on oeis4.)