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 A362260 Maximum over 0 <= k <= n/2 of the number of permutations of two symbols occurring k and n-2*k times, respectively, where a permutation and its reversal are counted only once. 2
 1, 1, 1, 1, 2, 2, 4, 6, 9, 12, 19, 28, 44, 66, 110, 170, 255, 396, 651, 1001, 1519, 2520, 4032, 6216, 9752, 15912, 25236, 38760, 63090, 101850, 160050, 248710, 408760, 653752, 1021735, 1634776, 2656511, 4218786, 6562556, 10737090, 17299646, 27313650, 43249115 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Also, a(n) is the maximum number of ways in which a set of integer-sided squares can tile an n X 2 rectangle, up to rotations and reflections. LINKS Robert Israel, Table of n, a(n) for n = 0..4771 FORMULA a(n) >= A073028(n)/2. EXAMPLE For n = 8, the maximum a(8) = 9 is obtained for k = 2. The corresponding permutations of 2 2's and 4 1's are 221111, 212111, 211211, 211121, 211112, 122111, 121211, 121121, and 112211. MAPLE f:= proc(n) local k, v, m, w; m:= 0: for k from 0 to n/2 do v:= binomial(n-k, k); if n:: even and k::even then w:= binomial((n-k)/2, k/2) elif (n-k)::odd then w:=binomial((n-k-1)/2, floor(k/2)) else w:= 0 fi; m:= max(m, (v+w)/2); od; m end proc: map(f, [\$0..50]); # Robert Israel, Oct 25 2023 CROSSREFS Row maxima of A102541. Second column of A362258. Cf. A001224, A073028, A361224 (rectangular pieces). Sequence in context: A035564 A240065 A237755 * A306730 A209603 A192684 Adjacent sequences: A362257 A362258 A362259 * A362261 A362262 A362263 KEYWORD nonn AUTHOR Pontus von Brömssen, Apr 15 2023 STATUS approved

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Last modified August 4 13:09 EDT 2024. Contains 374921 sequences. (Running on oeis4.)