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

%I #23 Sep 08 2022 08:46:13

%S 2,4,26,240,2882,42560,745418,15097600,347066882,8926258176,

%T 253930611002,7916100448256,268352394448322,9828088361009152,

%U 386707997366768618,16268790735900180480,728714136550643404802,34624041592426892361728

%N a(n) = n^n - (n-2)^n.

%C 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).

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

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

%p A262067:=n->n^n - (n-2)^n: seq(A262067(n), n=1..20); # _Wesley Ivan Hurt_, Sep 10 2015

%t Array[#^# - (# - 2)^# &, {18}] (* _Michael De Vlieger_, Sep 10 2015 *)

%o (PARI) a(n) = n^n - (n-2)^n;

%o vector(40, n, a(n))

%o (Magma) [n^n - (n-2)^n : n in [1..20]]; // _Wesley Ivan Hurt_, Sep 10 2015

%Y Cf. A000312, A008788.

%Y 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).

%K nonn,easy

%O 1,1

%A _Altug Alkan_, Sep 10 2015