A328652 Number of unlabeled loopless multigraphs with n edges covering four vertices.

0, 1, 3, 7, 13, 25, 40, 65, 99, 146, 208, 294, 399, 538, 711, 926, 1188, 1513, 1896, 2361, 2910, 3557, 4312, 5199, 6214, 7392, 8739, 10276, 12019, 14002, 16224, 18732, 21537, 24669, 28152, 32031, 36309, 41047, 46263, 51997, 58282, 65176, 72688, 80894, 89820, 99518

Offset: 1

Author

Andrew Howroyd, Oct 23 2019

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,0,-2,-2,3,0,3,-2,-2,0,0,2,-1).

Crossrefs

Column k=4 of A309936.

Cf. A001399, A003082.

Programs

Mathematica

LinearRecurrence[{2,0,0,-2,-2,3,0,3,-2,-2,0,0,2,-1},{0,1,3,7,13,25,40,65,99,146,208,294,399,538},50] (* Harvey P. Dale, Mar 06 2021 *)

PARI

concat([0], Vec((1 + x + x^2 - x^3 + x^4 - 2*x^5 + 2*x^6)/((1 - x)^6*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2) + O(x^40)))

Formula

a(n) = A003082(n) - A001399(n).

a(n) = 2*a(n-1) - 2*a(n-4) - 2*a(n-5) + 3*a(n-6) + 3*a(n-8) - 2*a(n-9) - 2*a(n-10) + 2*a(n-13) - a(n-14) for n > 14.

G.f.: x^2*(1 + x + x^2 - x^3 + x^4 - 2*x^5 + 2*x^6)/((1 - x)^6*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2).