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 A257198 Number of permutations of length n having exactly one descent such that the first element of the permutation is an odd number. 1
 0, 0, 2, 6, 16, 36, 78, 162, 332, 672, 1354, 2718, 5448, 10908, 21830, 43674, 87364, 174744, 349506, 699030, 1398080, 2796180, 5592382, 11184786, 22369596, 44739216, 89478458, 178956942, 357913912, 715827852, 1431655734, 2863311498, 5726623028 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2). FORMULA a(n) = 2*floor((2*2^n-3*n-1)/6). a(n) = 2*A178420(n-1). a(n) = A000295(n)-A000975(n-1). From Colin Barker, Apr 19 2015: (Start) a(n) = (-3-(-1)^n+2^(2+n)-6*n)/6. a(n) = 3*a(n-1)-a(n-2)-3*a(n-3)+2*a(n-4). G.f.: -2*x^3 / ((x-1)^2*(x+1)*(2*x-1)). (End) EXAMPLE a(3)=2: (1 3 2, 3 1 2). a(4)=6: (1 2 4 3, 1 3 2 4, 1 4 2 3, 1 3 4 2, 3 1 2 4, 3 4 1 2). MATHEMATICA Table[2 Floor[(2 2^n - 3 n - 1) / 6], {n, 50}] (* Vincenzo Librandi, Apr 18 2015 *) PROG (MAGMA) [2*Floor((2*2^n-3*n-1)/6): n in [1..40]]; // Vincenzo Librandi, Apr 18 2015 (PARI) concat([0, 0], Vec(-2*x^3/((x-1)^2*(x+1)*(2*x-1)) + O(x^100))) \\ Colin Barker, Apr 19 2015 (PARI) a(n)=(2<

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Last modified October 20 03:11 EDT 2019. Contains 328244 sequences. (Running on oeis4.)