A178885 Partial sums of Berstel sequence (A007420).

0, 0, 1, 3, 3, -1, -1, 15, 31, -1, -65, -1, 255, 255, -513, -1025, 1023, 4095, -1, -12289, -8193, 32767, 49151, -65537, -196609, 65535, 655359, 262143, -1835009, -2097153, 4194303, 9437183, -6291457, -33554433, -4194305, 100663295, 83886079, -251658241

Offset: 0

Author

Jonathan Vos Post, Dec 28 2010

Keywords

• easy
• sign

Comments

The subsequence of unique primes begins 3, 31, -12289, -65537. What is the next prime in the sequence?

The next prime in the sequence is -113249697660929, followed by 289815643220546158591. - Harvey P. Dale, May 15 2016

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-6,8,-4).

Crossrefs

Cf. A007420.

Programs

Mathematica

LinearRecurrence[{3,-6,8,-4},{0,0,1,3},50] (* Harvey P. Dale, May 15 2016 *)

Formula

a(n) = Sum_{i=0..n} A007420(i) = Sum_{i=0..n} a(n+1) = 2*a(i)-4*a(i-1)+4*a(i-2).

G.f.: -x^2*(256*x^11-512*x^10+384*x^9-192*x^8+64*x^7-1) / ((x-1)*(4*x^3-4*x^2+2*x-1)). - Colin Barker, Apr 20 2013

Extensions

Corrected by Harvey P. Dale, May 15 2016