A325912 a(n) = (-1)^n * Sum_{k=0..n} (-1)^k*2^(2^k).

2, 2, 14, 242, 65294, 4294902002, 18446744069414649614, 340282366920938463444927863362353561842, 115792089237316195423570985008687907852929702298719625576012656144550776078094

Offset: 0

Author

Seiichi Manyama, Sep 08 2019

Keywords

• nonn

Examples

			a(0) = 2^1 = 2.
a(1) = 2^2  - 2^1 = 2.
a(2) = 2^4  - 2^2 + 2^1 = 14.
a(3) = 2^8  - 2^4 + 2^2 - 2^1 = 242.
a(4) = 2^16 - 2^8 + 2^4 - 2^2 + 2^1 = 65294.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..11
• Sylvia Wenmackers, On the Limits of Comparing Subset Sizes within N, J. Phil. Math. (2024) Vol. 1, 223-251. See p. 229.

Crossrefs

Cf. A001146, A060803, A325910.

Programs

Mathematica

a[n_] := (-1)^n * Sum[(-1)^k * 2^(2^k), {k, 0, n}]; Array[a, 9, 0] (* Amiram Eldar, May 07 2021 *)

PARI

{a(n) = (-1)^n*sum(k=0,n,(-1)^k*2^2^k)}

Formula

a(n) = A001146(n) - a(n-1).