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A370766
Number of signed permutations of length n with adjacent elements differing by more than 1.
4
1, 2, 4, 20, 156, 1540, 18268, 253380, 4024220, 72006788, 1433150940, 31402068292, 751081569820, 19471227247620, 543821277818972, 16278774958879940, 519912803924769948, 17646698226141369220, 634307673944308523740, 24070514898945667594308
OFFSET
0,2
COMMENTS
A signed permutation is a sequence (x_1,x_2,...,x_n) of integers such that {|x_1|,|x_2|,...|x_n|} = {1,2...,n}.
Adjacent elements that differ in sign will always differ by more than 1.
LINKS
FORMULA
a(n) = A370767(n) + A370767(n-1) for n > 0.
a(n) = (1+2*n)*a(n-1) + (1-2*n)*a(n-2) + (9-2*n)*a(n-3) + (-6+2*n)*a(n-4) for n >= 4.
EXAMPLE
In the following examples, the number of assignments of signs to each unsigned permutation is shown in parenthesis.
a(2) = 4: 12(2), 21(2). Total is 2 + 2 = 4.
a(3) = 20: 123(2), 132(4), 213(4), 231(4), 312(4), 321(2).
PROG
(PARI) a(n)=subst(serlaplace(polcoef((1 + x)/(1 + (1 - 2*y)*x + 2*y*x^2) + O(x*x^n), n)), y, 1)
CROSSREFS
Sequence in context: A303671 A330663 A377339 * A102087 A372234 A357671
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Mar 01 2024
STATUS
approved