A292022 a(n) = 4*n*(n^2 + 2).

12, 48, 132, 288, 540, 912, 1428, 2112, 2988, 4080, 5412, 7008, 8892, 11088, 13620, 16512, 19788, 23472, 27588, 32160, 37212, 42768, 48852, 55488, 62700, 70512, 78948, 88032, 97788, 108240, 119412, 131328, 144012, 157488, 171780, 186912, 202908, 219792, 237588

Offset: 1

Author

Eric W. Weisstein, Sep 07 2017

Keywords

• nonn
• easy

Comments

For n > 1, Wiener index of the 2n-crossed prism graph.

Links

• Eric Weisstein's World of Mathematics, Crossed Prism Graph.
• Eric Weisstein's World of Mathematics, Wiener Index.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A006527, A054602, A217873.

Programs

Mathematica

Table[4 n (n^2 + 2), {n, 50}]
LinearRecurrence[{4, -6, 4, -1}, {12, 48, 132, 288}, 20]
CoefficientList[Series[(12 (1 + x^2))/(-1 + x)^4, {x, 0, 20}], x]

Formula

a(n) = 4*n*(n^2 + 2).

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

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

From Elmo R. Oliveira, Aug 09 2025: (Start)

E.g.f.: 4*x*(3 + 3*x + x^2)*exp(x).

a(n) = 12*A006527(n) = 4*A054602(n) = 3*A217873(n). (End)