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A223659 Number of unimodal maps [1..n]->[0..3]. 19

%I #37 Feb 11 2024 23:45:33

%S 1,4,16,50,130,296,610,1163,2083,3544,5776,9076,13820,20476,29618,

%T 41941,58277,79612,107104,142102,186166,241088,308914,391967,492871,

%U 614576,760384,933976,1139440,1381300,1664546,1994665,2377673,2820148,3329264

%N Number of unimodal maps [1..n]->[0..3].

%C Column 1 of A223663.

%C Apparently also column 4 of A071920. - _R. J. Mathar_, May 17 2014

%H Alois P. Heinz, <a href="/A223659/b223659.txt">Table of n, a(n) for n = 0..10000</a> (terms n = 1..210 from R. H. Hardin)

%H Kyu-Hwan Lee and Se-jin Oh, <a href="http://arxiv.org/abs/1601.06685">Catalan triangle numbers and binomial coefficients</a>, arXiv:1601.06685 [math.CO], 2016.

%F Empirical: a(n) = (1/720)*n^6 + (1/48)*n^5 + (23/144)*n^4 + (9/16)*n^3 + (241/180)*n^2 + (11/12)*n + 1 = 1 + n*(n+1)*(n^4 + 14*n^3 + 101*n^2 + 304*n + 660)/720.

%F Empirical g.f.: 1-x*(x^2-2*x+2)*(x^4-4*x^3+6*x^2-4*x+2) / (x-1)^7. - _R. J. Mathar_, May 14 2014

%e Some solutions for n=3:

%e 2 2 0 1 1 3 1 0 3 1 2 1 2 1 0 2

%e 2 2 1 3 3 3 3 2 2 2 2 3 0 1 1 1

%e 2 0 2 2 0 1 3 3 1 0 3 1 0 1 1 0

%Y Cf. A071920, A223663, A223718.

%K nonn

%O 0,2

%A _R. H. Hardin_, Mar 25 2013

%E a(0)=1 prepended by _Alois P. Heinz_, Feb 11 2024

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)