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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<<n-3*n-1)\6*2 \\ Charles R Greathouse IV, Apr 21 2015

CROSSREFS

Cf. A178420, A000295, A000975.

Sequence in context: A178523 A270810 A227035 * A053210 A066641 A265106

Adjacent sequences:  A257195 A257196 A257197 * A257199 A257200 A257201

KEYWORD

nonn,easy

AUTHOR

Ran Pan, Apr 18 2015

STATUS

approved

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Last modified September 26 06:24 EDT 2017. Contains 292502 sequences.