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

1,3

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).

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).

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 *)

Prog

(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)))

Crossrefs

Column k=4 of A309936.

Cf. A001399, A003082.

Sequence in context: A056764 A360783 A026103 * A301854 A092463 A259343

Adjacent sequences: A328649 A328650 A328651 * A328653 A328654 A328655

Keyword

nonn,easy

Author

Andrew Howroyd, Oct 23 2019

Status

approved