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A123245 Triangle A079487 with reversed rows.

%I A123245 #46 Apr 04 2025 15:38:22
%S A123245 1,1,1,1,1,1,1,1,2,1,1,2,2,2,1,1,2,3,3,3,1,1,3,4,5,4,3,1,1,3,5,7,7,6,
%T A123245 4,1,1,4,7,10,11,10,7,4,1,1,4,8,13,16,17,14,10,5,1,1,5,11,18,24,26,24,
%U A123245 18,11,5,1
%N A123245 Triangle A079487 with reversed rows.
%C A123245 Row sums give Fibonacci numbers (A000045).
%H A123245 Sébastien Labbé and Mélodie Lapointe, <a href="https://doi.org/10.5070/C62156881">The q-analog of the Markoff injectivity conjecture over the language of a balanced sequence</a>, Comb. Theor. (2022) Vol. 2, No. 1, #9. See also <a href="https://arxiv.org/abs/2106.15886">arXiv:2106.15886</a> [math.CO], 2021.
%H A123245 Sophie Morier-Genoud and Valentin Ovsienko, <a href="https://arxiv.org/abs/1812.00170">q-deformed rationals and q-continued fractions</a>, arXiv:1812.00170 [math.CO], 2018-2020.
%H A123245 Sophie Morier-Genoud and Valentin Ovsienko, <a href="https://arxiv.org/abs/1908.04365">On q-deformed real numbers</a>, arXiv:1908.04365 [math.QA], 2019.
%H A123245 Sophie Morier-Genoud and Valentin Ovsienko, <a href="https://hal.archives-ouvertes.fr/hal-02270545/">q-deformed rationals and q-continued fractions</a>, (2019) [math].
%H A123245 Sophie Morier-Genoud and Valentin Ovsienko, <a href="https://arxiv.org/abs/2011.10809">Quantum real numbers and q-deformed Conway-Coxeter friezes</a>, arXiv:2011.10809 [math.QA], 2020.
%H A123245 Sophie Morier-Genoud and Valentin Ovsienko, <a href="https://arxiv.org/abs/2503.23834">q-deformed rationals and irrationals</a>, arXiv:2503.23834 [math.CO], 2025. See p. 7.
%H A123245 Valentin Ovsienko, <a href="https://amathr.org/wp-content/uploads/2023/03/QOMBINUMReview-1.pdf">Modular invariant q-deformed numbers: first steps</a>, 2023.
%F A123245 p(k, x) = x*p(k - 1, x) + p(k - 2, x) for k even, otherwise p(k, x) = p(k - 1, x) + x^2*p(k - 2, x).
%e A123245 {1},
%e A123245 {1, 1},
%e A123245 {1, 1, 1},
%e A123245 {1, 1, 2, 1},
%e A123245 {1, 2, 2, 2, 1},
%e A123245 {1, 2, 3, 3, 3, 1},
%e A123245 {1, 3, 4, 5, 4, 3, 1},
%e A123245 {1, 3, 5, 7, 7, 6, 4, 1},
%e A123245 {1, 4, 7, 10, 11, 10, 7, 4, 1},
%e A123245 {1, 4, 8, 13, 16, 17, 14, 10, 5, 1},
%e A123245 {1, 5, 11, 18, 24, 26, 24, 18, 11, 5, 1}
%t A123245 p[0, x] = 1; p[1, x] = x + 1;
%t A123245 p[k_, x_] := p[k, x] = If[Mod[k, 2] == 0, x*p[k - 1, x] + p[k - 2, x], p[k - 1, x] + x^2*p[k - 2, x]];
%t A123245 Table[CoefficientList[p[n, x], x], {n, 0, 10}] // Flatten
%Y A123245 Cf. A000045, A079487, A078807, A078808, A077419.
%K A123245 nonn,tabl
%O A123245 0,9
%A A123245 _Roger L. Bagula_, Oct 07 2006
%E A123245 Edited by _Joerg Arndt_, May 26 2015
%E A123245 Offset corrected by _Andrey Zabolotskiy_, Sep 22 2017