A370966 a(n) = number of max-closed 2 X 2 X n relations.
1, 14, 122, 898, 6086, 39394, 248102, 1536178, 9409046, 57227074, 346467782, 2091269458, 12597590006, 75785795554, 455516874662, 2736312874738, 16430733386966, 98635853704834, 592021022116742, 3552949991056018, 21320996155647926, 127939164097754914, 767687740219762022
Offset: 0
Links
- Don Knuth, Parades and poly-Bernoulli bijections, Mar 31 2024. See (19.14) and (19.16).
- Filip Stappers, Problems concerning parades and poly-Bernoulli numbers, 2024. See Problem 10.
- Index entries for linear recurrences with constant coefficients, signature (15,-80,180,-144).
Formula
From Filip Stappers, Aug 19 2024: (Start)
a(n) = 35/6*6^n - 6*4^n + 2/3*3^n + 1/2*2^n.
G.f.: (1-z)*(1-8*z^2) / ((1-6*z)*(1-4*z)*(1-3*z)*(1-2*z)). (End)
E.g.f.: exp(2*x)*(3 + 4*exp(x) - 36*exp(2*x) + 35*exp(4*x)). - Stefano Spezia, Aug 20 2024
Extensions
a(7)-a(9) from Michael S. Branicky, Apr 07 2024
a(10) from Michael S. Branicky, Apr 08 2024
a(11) from Michael S. Branicky, Apr 22 2024
More terms from Filip Stappers, Aug 14 2024
a(0)=1 prepended by Filip Stappers, Aug 19 2024