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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.

%I A038718 #39 Nov 01 2024 12:05:40
%S A038718 1,1,2,4,6,9,14,21,31,46,68,100,147,216,317,465,682,1000,1466,2149,
%T A038718 3150,4617,6767,9918,14536,21304,31223,45760,67065,98289,144050,
%U A038718 211116,309406,453457,664574,973981,1427439,2092014,3065996,4493436,6585451
%N 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.
%C A038718 This sequence is the number of digits of each term of A061583. - _Dmitry Kamenetsky_, Jan 17 2009
%H A038718 Michael De Vlieger, <a href="/A038718/b038718.txt">Table of n, a(n) for n = 1..6023</a>
%H A038718 Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, <a href="https://ceur-ws.org/Vol-3792/paper19.pdf">Integer sequences from k-iterated line digraphs</a>, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
%H A038718 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-1).
%F A038718 From _Joseph Myers_, Feb 03 2004: (Start)
%F A038718 G.f.: (1 -x +x^2)/(1-2*x+x^2-x^3+x^4).
%F A038718 a(n) = a(n-1) + a(n-3) + 1. (End)
%F A038718 a(n) = Sum_{i=1..n} A058278(i) = A097333(n) - 1. - _R. J. Mathar_, Oct 16 2010
%t A038718 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 *)
%o A038718 (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
%Y A038718 Cf. A003274, A003410.
%K A038718 nonn,easy
%O A038718 1,3
%A A038718 _John W. Layman_, May 02 2000
%E A038718 More terms from _Joseph Myers_, Feb 03 2004