A241498 q-Lucas numbers with q=2.

2, 1, 3, 5, 17, 57, 329, 2153, 23209, 298793, 6240297, 159222313, 6549286441, 332636583465, 27158513845801, 2752117405591081, 447717208255194665, 90629100354663736873, 29432224060567101302313

Offset

0,1

Comments

a(n) = 2k+1, where apparently k = 8m, m odd for n > 3.

More generally, a(k) is congruent to a(n) modulo 2^(n-1) for any k > n. - Charlie Neder, Mar 09 2019

Links

Table of n, a(n) for n=0..18.

Hao Pan, Congruences for q-Lucas Numbers, Electron. J. Combin., 20, Issue 2 (2013), P29.

Formula

Recurrence: a(n) = a(n-1) + 2^(n-2)*a(n-2), starting 2, 1.

Prog

(Sage) # sage -i ore_algebra
from ore_algebra import *
R.<x> = QQ['x']; A.<Qx> = OreAlgebra(R, 'Qx', q=2)
print((Qx^2 - Qx - x).to_list([2, 1], 10))

Crossrefs

Cf. A015459, A241497.

Sequence in context: A144057 A272891 A219274 * A143581 A096871 A077890

Adjacent sequences: A241495 A241496 A241497 * A241499 A241500 A241501

Keyword

nonn

Author

Ralf Stephan, Apr 24 2014

Status

approved