A376768 a(1) = 2; thereafter, a(n) = c*A376767(n-1) + 1, where c=4 if n is even, c=2 if n is odd.

2, 5, 11, 221, 24311, 1182000821, 698562969831336611, 975980445639153806859347417915257421, 476268915135000629546288739757931900755190480621127468115605921390156911

Offset: 1

Author

N. J. A. Sloane, Nov 03 2024

Keywords

• nonn

Comments

This is the sequence of dampening coefficients for the divergent series 1 + 2 + 1 + 2 + 1 + 2 + ...

Links

• Paolo Xausa, Table of n, a(n) for n = 1..12
• N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides

Crossrefs

Cf. A374663, A376767.

Programs

Mathematica

A376767[n_] := A376767[n] = If[n == 1, 1, If[OddQ[n], 2, 4]*#^2 + # & [A376767[n-1]]];
A376768[n_] := If[n == 1, 2, If[OddQ[n], 2, 4]*A376767[n-1] + 1];
Array[A376768, 10] (* Paolo Xausa, Dec 16 2024 *)

Extensions

Definition corrected by N. J. A. Sloane, Dec 15 2024 - thanks to Paolo Xausa for noticing the error.