A323709 a(n) is the number of perfect matchings in the circulant graph on 2*n vertices with jumps 1, 2, and 3.

2, 3, 15, 60, 144, 336, 788, 1852, 4348, 10212, 23984, 56328, 132292, 310700, 729708, 1713788, 4024992, 9453072, 22201428, 52142140, 122460716, 287610500, 675480288, 1586428936, 3725877444, 8750573324, 20551543804, 48267231996, 113360130352, 266236919376, 625282425300, 1468534537980

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..2693

Wikipedia, Circulant graph

Index entries for linear recurrences with constant coefficients, signature (2,1,0,-1).

Formula

G.f.: (2*x - x^2 + 7*x^3 + 27*x^4 + 11*x^5 - 9*x^6 - 13*x^7)/(1 - 2*x - x^2 + x^4).

Maple

f:= gfun:-rectoproc({a(n) = 2*a(n-1)+a(n-2)- a(n-4), a(1) = 2, a(2) = 3, a(3) = 15, a(4) = 60, a(5) = 144, a(6) = 336, a(7) = 788}, a(n), remember):
map(f, [$1..30]);

Mathematica

a = DifferenceRoot[Function[{a, n}, {a[n]-a[n+2]-2*a[n+3]+a[n+4] == 0, a[1] == 2, a[2] == 3, a[3] == 15, a[4] == 60, a[5] == 144, a[6] == 336, a[7] == 788}]];
Table[a[n], {n, 1, 32}] (* Jean-François Alcover, Aug 27 2022 *)

Crossrefs

Sequence in context: A151369 A143885 A172012 * A338308 A047014 A027519

Adjacent sequences: A323706 A323707 A323708 * A323710 A323711 A323712

Keyword

nonn,easy

Author

Robert Israel, Jan 24 2019

Status

approved