A262067 a(n) = n^n - (n-2)^n.

2, 4, 26, 240, 2882, 42560, 745418, 15097600, 347066882, 8926258176, 253930611002, 7916100448256, 268352394448322, 9828088361009152, 386707997366768618, 16268790735900180480, 728714136550643404802, 34624041592426892361728

Offset: 1

Author

Altug Alkan, Sep 10 2015

Keywords

• nonn
• easy

Comments

Inspired by multi-dimensional cubes: For n>1, the number of lattice points on the surface of a k-dimensional cube with side-length n is f(n,k) = n^k - (n-2)^k. a(n) = f(n,n).

Examples

			For n = 2, a(n) = n^n - (n-2)^n = 2^2 - (2-2)^2 = 4.
		

Crossrefs

Cf. A000312, A008788.

For sequences with "Number of points on surface of k-dimensional cube," cf. A130130 (k=1), A008574 (k=2, shifted), A005897 (k=3), A008511 (k=4), A008512 (k=5), A008513 (k=6).

Programs

Magma

[n^n - (n-2)^n : n in [1..20]]; // Wesley Ivan Hurt, Sep 10 2015

Maple

A262067:=n->n^n - (n-2)^n: seq(A262067(n), n=1..20); # Wesley Ivan Hurt, Sep 10 2015

Mathematica

Array[#^# - (# - 2)^# &, {18}] (* Michael De Vlieger, Sep 10 2015 *)

PARI

a(n) = n^n - (n-2)^n;
vector(40, n, a(n))

Formula

a(n) = A000312(n) - A008788(n-2).