OFFSET
3,2
LINKS
Ivaylo Kortezov, Sets of Non-self-intersecting Paths Connecting the Vertices of a Convex Polygon, Mathematics and Informatics, Vol. 65, No. 6, 2022.
Index entries for linear recurrences with constant coefficients, signature (48,-1040,13440,-115296,691200,-2967296,9185280,-20336896,31395840,-32071680,19464192,-5308416).
FORMULA
a(n) = n*(n-1)*(n-2)*2^(n-10)*(3^(n-4) + 3*2^(n-3) + 9) for n >= 4.
EXAMPLE
a(5) = 5!/(2!2!2!) + binomial(5,2)*3 = 15 + 30 = 45; the first summand corresponds to the case when two of the paths have two nodes each and one path has one node; the second corresponds to the case when two of the paths have one node each and one path has three nodes.
MATHEMATICA
LinearRecurrence[{48, -1040, 13440, -115296, 691200, -2967296, 9185280, -20336896, 31395840, -32071680, 19464192, -5308416}, {1, 6, 45, 315, 2205, 15624, 111888, 807840, 5868720, 42799680, 312504192, 2278418688, 16549827840}, 23] (* Stefano Spezia, Jan 22 2023 *)
PROG
(PARI) a(n) = if(n==3, 1, n*(n-1)*(n-2)*2^(n-10)*(3^(n-4) + 3*2^(n-3) + 9)) \\ Andrew Howroyd, Jan 23 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ivaylo Kortezov, Jan 22 2023
STATUS
approved