A393462 Wiener index of the n-necklace graph.

0, 6, 50, 162, 388, 750, 1302, 2058, 3080, 4374, 6010, 7986, 10380, 13182, 16478, 20250, 24592, 29478, 35010, 41154, 48020, 55566, 63910, 73002, 82968, 93750, 105482, 118098, 131740, 146334, 162030, 178746, 196640, 215622, 235858, 257250, 279972, 303918

Offset

0,2

Comments

Sequence extended to a(0) using the formula.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Necklace Graph.

Eric Weisstein's World of Mathematics, Wiener Index.

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

Formula

a(n)=n*(1+(-1)^n+12*n^2)/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.: 2*x*(3+19*x+28*x^2+19*x^3+3*x^4)/((-1+x)^4*(1+x)^2).

Mathematica

Table[n (1 + (-1)^n + 12 n^2)/2, {n, 0, 20}]
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {6, 50, 162, 388, 750, 1302}, {0, 20}]
CoefficientList[Series[2 x (3 + 19 x + 28 x^2 + 19 x^3 + 3 x^4)/((-1 + x)^4 (1 + x)^2), {x, 0, 20}], x]

Crossrefs

Sequence in context: A187670 A187462 A231270 * A062801 A035290 A138422

Adjacent sequences: A393459 A393460 A393461 * A393463 A393464 A393465

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 15 2026

Status

approved