

A048162


Expansion of (1  x + 3*x^3  2*x^4  3*x^5)/(1  2*x + x^3).


2



1, 1, 2, 6, 9, 13, 20, 31, 49, 78, 125, 201, 324, 523, 845, 1366, 2209, 3573, 5780, 9351, 15129, 24478, 39605, 64081, 103684, 167763, 271445, 439206, 710649, 1149853, 1860500, 3010351, 4870849, 7881198, 12752045, 20633241, 33385284
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OFFSET

0,3


COMMENTS

Number of permutations of 1..n such that each position is fixed or moves to an adjacent position (with n considered adjacent to 1). For example, a(4) = 9 because there is the identity; 2 cyclic permutations; 4 swaps of one pair of adjacent entries; and 2 swaps of two pairs of adjacent entries.  Joshua Zucker, Nov 13 2003


REFERENCES

Lehmer, D. H.; Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755770. NorthHolland, Amsterdam, 1970.


LINKS

Table of n, a(n) for n=0..36.


FORMULA

For n>4, a(n) = a(n1) + a(n2)  2.  Joshua Zucker, Nov 13 2003
a(n) = Fibonacci(n+1) + Fibonacci(n1) + 2, for n>2.  Jessa Lee (jessal(AT)comcast.net), Nov 25 2003
For n > 2, a(n)=A001610(n1)  3.  Toby Gottfried, Apr 13 2013


MATHEMATICA

CoefficientList[Series[(1x+3x^32x^43x^5)/(12x+x^3), {x, 0, 40}], x] (* or *) Join[{1, 1, 2}, #[[3]]+#[[1]]+2&/@Partition[Fibonacci[Range[2, 50]], 3, 1]] (* Harvey P. Dale, Apr 06 2017 *)


CROSSREFS

3rd column of A008305.
Cf. A001610.
Sequence in context: A076522 A094111 A181021 * A226823 A171866 A297833
Adjacent sequences: A048159 A048160 A048161 * A048163 A048164 A048165


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Second formula corrected by David Radcliffe, Jan 16 2011


STATUS

approved



