A038718 Number of permutations P of {1,2,...,n} such that P(1)=1 and |P^-1(i+1)-P^-1(i)| equals 1 or 2 for i=1,2,...,n-1.

1, 1, 2, 4, 6, 9, 14, 21, 31, 46, 68, 100, 147, 216, 317, 465, 682, 1000, 1466, 2149, 3150, 4617, 6767, 9918, 14536, 21304, 31223, 45760, 67065, 98289, 144050, 211116, 309406, 453457, 664574, 973981, 1427439, 2092014, 3065996, 4493436, 6585451

Offset

1,3

Comments

This sequence is the number of digits of each term of A061583. - Dmitry Kamenetsky, Jan 17 2009

Links

Table of n, a(n) for n=1..41.

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-1).

Formula

From Joseph Myers, Feb 03 2004: (Start)

G.f.: (1 -x +x^2)/(1-2*x+x^2-x^3+x^4).

a(n) = a(n-1) + a(n-3) + 1. (End)

a(n) = Sum_{i=1..n} A058278(i) = A097333(n) - 1. - R. J. Mathar, Oct 16 2010

Mathematica

LinearRecurrence[{2, -1, 1, -1}, {1, 1, 2, 4}, 50] (* or *) CoefficientList[ Series[(x^2-x+1)/(x^4-x^3+x^2-2x+1), {x, 0, 50}], x] (* Harvey P. Dale, Apr 24 2011 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 1, -1, 2]^(n-1)*[1; 1; 2; 4])[1, 1] \\ Charles R Greathouse IV, Apr 07 2016

Crossrefs

Cf. A003274, A003410.

Sequence in context: A097197 A260600 A119737 * A042942 A256968 A005687

Adjacent sequences: A038715 A038716 A038717 * A038719 A038720 A038721

Keyword

nonn,easy

Author

John W. Layman, May 02 2000

Extensions

More terms from Joseph Myers, Feb 03 2004

Status

approved