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A333833 Number of permutations p of [n] such that |p(i) - p(i-1)| <= 2 and |p(i) - p(i-2)| <= 3. 3
1, 1, 2, 6, 12, 14, 18, 28, 42, 56, 74, 102, 144, 200, 274, 376, 520, 720, 994, 1370, 1890, 2610, 3604, 4974, 6864, 9474, 13078, 18052, 24916, 34390, 47468, 65520, 90436, 124826, 172294, 237814, 328250, 453076, 625370, 863184, 1191434, 1644510, 2269880, 3133064 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..7141

Alois P. Heinz, Animation of a(10) = 74 permutations

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1).

FORMULA

G.f.: -(2*x^8+4*x^7+2*x^6+x^5+5*x^4+4*x^3+x^2+1)/(x^4+x-1).

a(n) = 2*A302510(n-2) for n >= 6.

Limit_{n-> infinity} a(n+1)/a(n) = A086106.

EXAMPLE

a(5) = 14: 12345, 12354, 12435, 12453, 13245, 21345, 31245, 35421, 45321, 53421, 54213, 54231, 54312, 54321.

a(6) = 18: 123456, 123465, 123546, 123564, 124356, 132456, 213456, 213465, 312456, 465321, 564312, 564321, 645321, 653421, 654213, 654231, 654312, 654321.

CROSSREFS

Cf. A003274, A086106, A174700, A263690, A263696, A302510, A307269, A328648.

Sequence in context: A154712 A079849 A260907 * A057895 A111369 A190503

Adjacent sequences:  A333830 A333831 A333832 * A333834 A333835 A333836

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Apr 07 2020

STATUS

approved

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Last modified July 6 23:56 EDT 2020. Contains 335484 sequences. (Running on oeis4.)