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A130783 Maximum value of the n-th difference of a permutation of 0..n. 3
0, 1, 3, 10, 25, 66, 154, 372, 837, 1930, 4246, 9516, 20618, 45332, 97140, 210664, 447661, 960858, 2028478, 4319100, 9070110, 19188796, 40122028, 84438360, 175913250, 368603716, 765561564, 1598231992, 3310623412, 6889682280, 14238676712, 29551095248 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n>1, a(n) is also the maximum value of the n-th difference of a permutation of 1..n. - Michel Marcus, Apr 15 2017

LINKS

Fung Lam, Table of n, a(n) for n = 0..3000

F. Disanto, A. Frosini, S. Rinaldi, Square involutions, J. Int. Seq. 14 (2011) # 11.3.5.

FORMULA

a(n) = (n+1)*(2^(n-1)-binomial(n-1,n/2)) if n is even else ((n+1)/2)*(2^n-binomial(n,(n+1)/2)). - Vladeta Jovovic, Aug 23 2007

a(n) = (n+1)*(2^n-binomial(n,[n/2]))/2, where [x] is floor. - Graeme McRae, Jan 30, 2012

G.f.: (1-sqrt((1-2*x)/(1+2*x)))/(2*(1-2*x)^2). - Vladeta Jovovic, Aug 24 2007

Asymptotics: a(n) ~ 2^(n-1)*(n+1-sqrt(2*n/Pi)). - Fung Lam, Mar 28 2014

Recurrence: (n-1)*n*a(n) = 2*(n-1)*(n+1)*a(n-1) + 4*(n-2)*n*a(n-2) - 8*(n-1)*n*a(n-3). - Vaclav Kotesovec, Mar 28 2014

EXAMPLE

a(1)=1 because 0 1 has a first difference of 1; a(2)=3 because 2 0 1 has a second difference of 3.

MAPLE

A130783:=n->(n+1)*(2^n-binomial(n, floor(n/2)))/2; seq(A130783(n), n=0..50); # Wesley Ivan Hurt, Nov 25 2013

MATHEMATICA

Table[(n + 1) (2^n - Binomial[n, Floor[n/2]])/2, {n, 0, 50}] (* Wesley Ivan Hurt, Nov 25 2013 *)

PROG

(PARI) a(n)=(n+1)*(2^n-binomial(n, n\2))/2 \\ Charles R Greathouse IV, Jan 30 2012

CROSSREFS

Cf. A000346, A033504.

Sequence in context: A089117 A176610 A026965 * A026975 A296668 A026985

Adjacent sequences:  A130780 A130781 A130782 * A130784 A130785 A130786

KEYWORD

nonn,easy

AUTHOR

R. H. Hardin, Aug 19 2007

STATUS

approved

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Last modified November 19 00:12 EST 2019. Contains 329310 sequences. (Running on oeis4.)