A052482 a(n) = 2^(n-2)*binomial(n+1,2).

3, 12, 40, 120, 336, 896, 2304, 5760, 14080, 33792, 79872, 186368, 430080, 983040, 2228224, 5013504, 11206656, 24903680, 55050240, 121110528, 265289728, 578813952, 1258291200, 2726297600, 5888802816, 12683575296, 27246198784, 58384711680, 124822487040

Offset: 2

Author

N. J. A. Sloane, Mar 16 2000

Keywords

• nonn
• easy

Comments

Also the number of 4-cycles in the (n+1)-folded cube graph for n > 3. - Eric W. Weisstein, Mar 21 2018

Links

• Colin Barker, Table of n, a(n) for n = 2..1000
• Eric Weisstein's World of Mathematics, Folded Cube Graph
• Eric Weisstein's World of Mathematics, Graph Cycle
• Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

Crossrefs

Essentially the same as A080929.

Cf. A301459 (6-cycles in the n-folded cube graph).

Programs

Mathematica

Table[2^(n - 2) Binomial[n + 1, 2], {n, 2, 28}] (* Michael De Vlieger, Sep 21 2017 *)
LinearRecurrence[{6, -12, 8}, {3, 12, 40}, 20] (* Eric W. Weisstein, Mar 21 2018 *)
CoefficientList[Series[(-3 + 6 x - 4 x^2)/(-1 + 2 x)^3, {x, 0, 20}], x] (* Eric W. Weisstein, Mar 21 2018 *)

PARI

Vec(x^2*(3 - 6*x + 4*x^2) / (1 - 2*x)^3 + O(x^40)) \\ Colin Barker, Sep 22 2017

Formula

a(n) = (1/2) * Sum_{k=0..n-1} Sum_{i=0..n-1} (k+1) * C(n-1,i). - Wesley Ivan Hurt, Sep 20 2017

From Colin Barker, Sep 22 2017: (Start)

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

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

a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) for n>4.

(End)