OFFSET
0,5
LINKS
Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-1,-1,1,-4,-2,-3,-1,1,1,1).
FORMULA
G.f.: (x^3-x-2)*x^4 / ((x+1) *(x^6-x^5+x^4-3*x^3+3*x^2-3*x+1) *(x^4+x^3+x^2+x-1)).
EXAMPLE
a(4) = 2: 4231, 4321.
a(5) = 7: 15342, 15432, 35142, 42315, 42513, 43215, 45312.
a(6) = 19: 126453, 126543, 146253, 153426, 153624, 154326, 156423, 216453, 216543, 351426, 351624, 423156, 423165, 425136, 426153, 432156, 432165, 453126, 456123.
MAPLE
gf:= (x^3-x-2)*x^4 / ((x+1)*(x^6-x^5+x^4-3*x^3+3*x^2-3*x+1)*
(x^4+x^3+x^2+x-1)):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..40);
MATHEMATICA
CoefficientList[Series[(x^3 - x - 2) x^4/((x + 1) (x^6 - x^5 + x^4 - 3 x^3 + 3 x^2 - 3 x + 1) (x^4 + x^3 + x^2 + x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 09 2014 *)
LinearRecurrence[{3, -1, -1, 1, -4, -2, -3, -1, 1, 1, 1}, {0, 0, 0, 0, 2, 7, 19, 47, 117, 284, 675}, 40] (* Harvey P. Dale, Jun 12 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Mar 07 2014
STATUS
approved