A323670 Irregular triangle of the coefficients P_(n,j) of Morier-Genoud and Ovsienko's polynomials P_n.

1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 3, 2, 1, 1, 3, 5, 6, 6, 5, 2, 1, 1, 3, 7, 11, 13, 13, 11, 7, 3, 1, 1, 4, 10, 18, 25, 29, 29, 24, 16, 9, 3, 1, 1, 4, 12, 25, 41, 56, 65, 65, 56, 41, 25, 12, 4, 1, 1, 5, 16, 37, 67, 101, 131, 148, 146, 126, 95, 61, 32, 14, 4, 1, 1

Offset

0,5

Comments

A q-deformation of the Pell numbers.

Links

Table of n, a(n) for n=0..73.

Sophie Morier-Genoud and Valentin Ovsienko, q-deformed rationals and q-continued fractions, arXiv:1812.00170 [math.CO], 2018-2020. See Section 6.3.

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

Wikipedia, Gaussian binomial coefficient

Index entries related to Gaussian binomial coefficients.

Formula

Coefficients of the polynomials defined by p(n) = p(n-2)*(4,2)_q - q^4*p(n-4) where (4,2)_q = 1+q+2*q^2+q^3+q^4, with p(0)=0, p(1)=1, p(2)=1+q, p(3)=1+q+2*q^2+q^3.

Example

Triangle begins:
1
1   1
1   2   1   1
1   2   3   3   2   1
1   3   5   6   6   5   2   1
1   3   7  11  13  13  11   7   3   1
1   4  10  18  25  29  29  24  16   9   3   1
...

Crossrefs

Cf. A079487, A123245.

Sequence in context: A272084 A003023 A156070 * A114731 A035389 A129176

Adjacent sequences: A323667 A323668 A323669 * A323671 A323672 A323673

Keyword

nonn,tabf

Author

Michael De Vlieger, Jan 23 2019

Status

approved