A111108 a(n) = A001333(n) - (-2)^(n-1), n > 0.

0, 5, 3, 25, 25, 131, 175, 705, 1137, 3875, 7095, 21649, 43225, 122435, 259423, 698625, 1541985, 4011971, 9107175, 23143825, 53559817, 133933475, 314086735, 776787009, 1838300625, 4512108515, 10745077143, 26237143825, 62749602745

Offset: 1

Author

Creighton Dement, Oct 14 2005

Keywords

• easy
• nonn

Comments

Conjecture: for odd primes p, p divides a(p). Note that (a(n)) and A001333 have different offsets.

The conjecture follows from the formula A001333(n) = ((1-sqrt(2))^n + (1+sqrt(2))^n)/2. - Max Alekseyev, Oct 16 2005

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,5,2).

Crossrefs

Cf. A001333, A000204.

Programs

Mathematica

LinearRecurrence[{0,5,2},{0,5,3},30] (* Harvey P. Dale, May 03 2022 *)

PARI

concat(0, Vec(x^2*(5 + 3*x) / ((1 + 2*x)*(1 - 2*x - x^2)) + O(x^35))) \\ Colin Barker, May 01 2019

Formula

From Colin Barker, Apr 30 2019: (Start)

G.f.: x^2*(5 + 3*x) / ((1 + 2*x)*(1 - 2*x - x^2)).

a(n) = 5*a(n-2) + 2*a(n-3) for n>3.

(End)