A337589 Expansion of (x^3-1+sqrt((x^4+x^3+4*x^2+x+1)*(x^2-x+1)))/(2*x^2).

1, 0, 0, 1, 0, -2, 1, 4, -5, -7, 18, 7, -55, 18, 146, -155, -322, 692, 476, -2446, 307, 7322, -6276, -18277, 33061, 33376, -129238, -10899, 420594, -276272, -1147125, 1742502, 2413761, -7448113, -2292774, 25986573, -11940263, -76138258, 96229907, 178087693, -450647034

Offset

0,6

Comments

Coefficients of [sqrt(2)]_q. See link.

Links

Table of n, a(n) for n=0..40.

Sophie Morier-Genoud and Valentin Ovsienko, Quantum real numbers and q-deformed Conway-Coxeter friezes, arXiv:2011.10809 [math.QA], 2020. See section 3.4.

Formula

D-finite with recurrence (n+2)*a(n) +4*(n-1)*a(n-2) +(-2*n+5)*a(n-3) +4*(n-4)*a(n-4) +(n-7)*a(n-6)=0. - R. J. Mathar, Aug 19 2022

Example

G.f. = 1 + x^3 - 2*x^5 + x^6 + 4*x^7 - 5*x^8 - 7*x^9 + 18*x^10 + ...

Prog

(PARI) my(x='x+O('x^45)); Vec((x^3-1+sqrt((x^4+x^3+4*x^2+x+1)*(x^2-x+1)))/(2*x^2))

Crossrefs

Sequence in context: A292388 A261035 A080030 * A125156 A119808 A021470

Adjacent sequences: A337586 A337587 A337588 * A337590 A337591 A337592

Keyword

sign

Author

Michel Marcus, Nov 25 2020

Status

approved