A390874 Molecular topological index of the n-necklace graph.

72, 372, 1080, 2472, 4680, 8028, 12600, 18768, 26568, 36420, 48312, 62712, 79560, 99372, 122040, 148128, 177480, 210708, 247608, 288840, 334152, 384252, 438840, 498672, 563400, 633828, 709560, 791448, 879048, 973260, 1073592, 1180992, 1294920, 1416372, 1544760

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Molecular Topological Index.

Eric Weisstein's World of Mathematics, Necklace Graph.

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Formula

a(n) = 3*n*(13 + (-1)^n + 12*n^2).

a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).

G.f.: 12*x*(6+19*x+22*x^2+19*x^3+6*x^4)/((-1+x)^4*(1+x)^2).

Mathematica

Table[3 n (13 + (-1)^n + 12 n^2), {n, 20}]
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {72, 372, 1080, 2472, 4680, 8028}, 20]
CoefficientList[Series[12 (6 + 19 x + 22 x^2 + 19 x^3 + 6 x^4)/((-1 + x)^4 (1 + x)^2), {x, 0, 20}], x]

Crossrefs

Sequence in context: A334902 A192792 A303621 * A084479 A084478 A187158

Adjacent sequences: A390871 A390872 A390873 * A390875 A390876 A390877

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 17 2026

Status

approved