login
A323799
Number of permutations p of [n] such that max_{j=1..n} |p(j)-j| = 3.
2
0, 10, 47, 157, 503, 1669, 5472, 17531, 55135, 172134, 535510, 1660795, 5133470, 15826173, 48706210, 149721544, 459820058, 1411142937, 4328181110, 13269541967, 40669595890, 124617708274, 381776661185, 1169438884559, 3581781480980, 10969462410857, 33592685042253
OFFSET
3,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-2,-2,6,-17,-16,-30,6,32,48,12,-16,-16,-9,2,-2,-2,2,1).
FORMULA
G.f.: x^4 *(x^11+x^10-3*x^9+x^8+4*x^7-4*x^6-4*x^5-5*x^4+11*x^3+11*x^2-7*x-10) / ((x-1) *(x^5 -2*x^3 -2*x+1) *(x^13 +3*x^12 +3*x^11 +5*x^10 +9*x^9 +7*x^8 -3*x^7 -19*x^6 -21*x^5 -13*x^4 -3*x^3 -3*x^2-x+1)).
a(n) = A002526(n) - A002524(n).
EXAMPLE
a(4) = 10: 2341, 2431, 3241, 3421, 4123, 4132, 4213, 4231, 4312, 4321.
CROSSREFS
Column k=3 of A130152.
Sequence in context: A253477 A143895 A281767 * A213575 A319491 A034443
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jan 28 2019
STATUS
approved