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 A114210 Number of derangements of [n] avoiding the patterns 123 and 231. 2
 0, 1, 1, 3, 4, 7, 8, 14, 13, 23, 20, 34, 28, 48, 37, 64, 48, 82, 60, 103, 73, 126, 88, 151, 104, 179, 121, 209, 140, 241, 160, 276, 181, 313, 204, 352, 228, 394, 253, 438, 280, 484, 308, 533, 337, 584, 368, 637, 400, 693, 433, 751, 468, 811, 504, 874, 541, 939 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n)=binomial(n,2)+1-A114208(n)-A114209(n) REFERENCES T. Mansour and A. Robertson, Refined restricted permutations avoiding subsets of patterns of length three, Annals of Combinatorics, 6, 2002, 407-418. LINKS Index entries for linear recurrences with constant coefficients, signature (-1,2,3,0,-3,-2,1,1). FORMULA (7n^2-18n+24)/24 if n mod 6 = 0; (n^2-1)/6 if n mod 6 = 1 or 5; (7n^2-18n+32)/24 if n mod 6 = 2 or 4; (n^2-3)/6 if n mod 6 = 3. G.f.: -x^2*(x^6+x^5+2*x^4+2*x^3+2*x^2+2*x+1) / ((x-1)^3*(x+1)^3*(x^2+x+1)). - Colin Barker, Aug 14 2013 EXAMPLE a(2)=1 because we have 21; a(3)=1 because we have 312; a(4)=3 because we have 2143, 4312 and 4321. MAPLE a:=proc(n) if n mod 6 = 0 then (7*n^2-18*n+24)/24 elif n mod 6 = 1 or n mod 6 = 5 then (n^2-1)/6 elif n mod 6 = 2 or n mod 6 = 4 then (7*n^2-18*n+32)/24 else (n^2-3)/6 fi end: seq(a(n), n=1..70); PROG (PARI) Vec(-x^2*(x^6+x^5+2*x^4+2*x^3+2*x^2+2*x+1)/((x-1)^3*(x+1)^3*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Aug 14 2013 CROSSREFS Cf. A114208, A114209. Sequence in context: A023054 A060023 A120355 * A073271 A117471 A217135 Adjacent sequences:  A114207 A114208 A114209 * A114211 A114212 A114213 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Nov 17 2005 STATUS approved

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Last modified August 20 04:17 EDT 2019. Contains 326139 sequences. (Running on oeis4.)