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

Author

John W. Layman, May 02 2000

Keywords

• nonn
• easy

Comments

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

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..6023
• Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, Integer sequences from k-iterated line digraphs, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-1).

Crossrefs

Cf. A003274, A003410.

Programs

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 *)

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

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

Extensions

More terms from Joseph Myers, Feb 03 2004