OFFSET
0,7
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
B. Nakamura, Approaches for enumerating permutations with a prescribed number of occurrences of patterns, arXiv 1301.5080 [math.CO], 2013.
B. Nakamura, A Maple package for enumerating n-permutations with r occurrences of the pattern 123 and s occurrences of the pattern 132 [Broken link]
Index entries for linear recurrences with constant coefficients, signature (14,-84,280,-560,672,-448,128).
FORMULA
G.f.: -(4*x^8-8*x^7+24*x^6-36*x^5+62*x^4-60*x^3+30*x^2-8*x+1)*x^5 / (2*x-1)^7. - Alois P. Heinz, Apr 03 2013
From Colin Barker, Nov 28 2018: (Start)
a(n) = (1/9)*2^(n-15) * (307008 - 247512*n + 78118*n^2 - 12087*n^3 + 937*n^4 - 33*n^5 + n^6) for n>6.
a(n) = 14*a(n-1) - 84*a(n-2) + 280*a(n-3) - 560*a(n-4) + 672*a(n-5) - 448*a(n-6) + 128*a(n-7) for n>13.
(End)
EXAMPLE
a(5) = 1: (1,4,3,2,5).
a(6) = 6: (2,5,4,3,1,6), (2,5,4,3,6,1), (3,5,1,4,6,2), (3,6,1,4,2,5), (5,1,4,3,2,6), (6,1,4,3,2,5).
MAPLE
# Programs can be obtained from the Nakamura link
MATHEMATICA
Join[{0, 0, 0, 0, 0, 1, 6}, LinearRecurrence[{14, -84, 280, -560, 672, -448, 128}, {30, 136, 566, 2176, 7808, 26440, 85332}, 33]] (* Jean-François Alcover, Nov 28 2018 *)
PROG
(PARI) concat([0, 0, 0, 0, 0], Vec(x^5*(1 - 8*x + 30*x^2 - 60*x^3 + 62*x^4 - 36*x^5 + 24*x^6 - 8*x^7 + 4*x^8) / (1 - 2*x)^7 + O(x^40))) \\ Colin Barker, Nov 28 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Brian Nakamura, Apr 03 2013
STATUS
approved