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 A024012 a(n) = 2^n - n^2. 24
 1, 1, 0, -1, 0, 7, 28, 79, 192, 431, 924, 1927, 3952, 8023, 16188, 32543, 65280, 130783, 261820, 523927, 1048176, 2096711, 4193820, 8388079, 16776640, 33553807, 67108188, 134216999, 268434672, 536870071, 1073740924, 2147482687, 4294966272, 8589933503, 17179868028, 34359737143 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS The sequence 2^(n-2) - (n-2)^2, n=7,8,... enumerates the number of non-isomorphic sequences of length n, with entries from {1,2,3} and no two adjacent entries the same, that contain each of the thirteen rankings of three players (111, 121, 112, 211, 122, 212, 221, 123, 132, 213, 231, 312, 321) as embedded order isomorphic subsequences. See the arXiv paper below for proof. If n=7, these sequences are 1213121, 1213212, 1231213, 1231231,1231321, 1232123, and 1232132, and for each case, there are 3!=6 isomorphs. - Anant Godbole, Feb 20 2013 REFERENCES GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See page 92. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Anant Godbole and Martha Liendo, Waiting time distribution for the emergence of superpatterns, arxiv 1302.4668 [math.PR], 2013. Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2). FORMULA G.f.: (1 - 4*x + 4*x^2 + x^3)/((1 - 2*x)*(1 - x)^3). - Vincenzo Librandi, Jul 13 2012 a(n) = 5*a(n - 1) - 9*a(n - 2) + 7*a(n - 3) - 2*a(n - 4). - Vincenzo Librandi, Jul 13 2012 MAPLE seq(2^n-n^2, n=0..35); # Zerinvary Lajos, Jul 01 2007 MATHEMATICA CoefficientList[Series[(1 - 4*x + 4*x^2 + x^3)/((1 - x)^3(1 - 2x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 13 2012 *) Table[2^n - n^2, {n, 0, 39}] (* Alonso del Arte, Dec 16 2012 *) PROG (Magma) [2^n-n^2: n in [0..30]]; // Vincenzo Librandi, Apr 29 2011 (PARI) a(n)=2^n-n^2 \\ Charles R Greathouse IV, Apr 17 2012 (Maxima) A024012(n):=2^n-n^2\$ makelist(A024012(n), n, 0, 20); /* Martin Ettl, Dec 18 2012 */ CROSSREFS Cf. A072180 (2^n - n^2 is prime), A075896 (primes of the form 2^n - n^2), A099481 (2^n - n^2 is a semiprime), A099482 (semiprimes of the form 2^n - n^2). Sequence in context: A341067 A061968 A223772 * A352900 A163705 A162595 Adjacent sequences: A024009 A024010 A024011 * A024013 A024014 A024015 KEYWORD sign,easy AUTHOR N. J. A. Sloane. EXTENSIONS More terms from Hugo Pfoertner, Oct 18 2004 STATUS approved

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Last modified February 28 14:45 EST 2024. Contains 370400 sequences. (Running on oeis4.)