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 A370966 a(n) = number of max-closed 2 X 2 X n relations. 1

%I #56 Aug 20 2024 18:12:22

%S 1,14,122,898,6086,39394,248102,1536178,9409046,57227074,346467782,

%T 2091269458,12597590006,75785795554,455516874662,2736312874738,

%U 16430733386966,98635853704834,592021022116742,3552949991056018,21320996155647926,127939164097754914,767687740219762022

%N a(n) = number of max-closed 2 X 2 X n relations.

%H Don Knuth, <a href="https://www-cs-faculty.stanford.edu/~knuth/papers/poly-Bernoulli.pdf">Parades and poly-Bernoulli bijections</a>, Mar 31 2024. See (19.14) and (19.16).

%H Filip Stappers, <a href="https://archive.org/details/parades_problems/">Problems concerning parades and poly-Bernoulli numbers</a>, 2024. See Problem 10.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (15,-80,180,-144).

%F From _Filip Stappers_, Aug 19 2024: (Start)

%F a(n) = 35/6*6^n - 6*4^n + 2/3*3^n + 1/2*2^n.

%F G.f.: (1-z)*(1-8*z^2) / ((1-6*z)*(1-4*z)*(1-3*z)*(1-2*z)). (End)

%F E.g.f.: exp(2*x)*(3 + 4*exp(x) - 36*exp(2*x) + 35*exp(4*x)). - _Stefano Spezia_, Aug 20 2024

%Y Cf. A370967, A371761.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Apr 04 2024

%E a(7)-a(9) from _Michael S. Branicky_, Apr 07 2024

%E a(10) from _Michael S. Branicky_, Apr 08 2024

%E a(11) from _Michael S. Branicky_, Apr 22 2024

%E More terms from _Filip Stappers_, Aug 14 2024

%E a(0)=1 prepended by _Filip Stappers_, Aug 19 2024

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Last modified September 10 16:20 EDT 2024. Contains 375790 sequences. (Running on oeis4.)