A190042 - OEIS

%I #8 May 04 2018 09:29:54

%S 2,8,10,18,16,30,22,40,31,49,36,64,41,71,53,81,55,97,61,103,74,112,75,

%T 131,80,134,96,144,94,164,100,166,117,175,114,198,119,197,139,207,133,

%U 231,139,229,160,238,153,265,158,260,182,270,172,298,178,292,203,301,192

%N Number of nondecreasing arrangements of 5 numbers in 0..n with the last equal to n and each after the second equal to the sum of one or two of the preceding three.

%C Row 3 of A190041.

%H R. H. Hardin, <a href="/A190042/b190042.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = -2*a(n-1) -2*a(n-2) +3*a(n-4) +4*a(n-5) +3*a(n-6) -2*a(n-8) -2*a(n-9) -a(n-10).

%F Empirical g.f.: x*(2 + 12*x + 30*x^2 + 54*x^3 + 66*x^4 + 66*x^5 + 46*x^6 + 26*x^7 + 9*x^8 + 3*x^9) / ((1 - x)^2*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2). - _Colin Barker_, May 04 2018

%e All solutions for n=3:

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

%e ..1....1....3....3....3....2....2....1....3....1

%e ..1....2....3....3....3....3....2....1....3....2

%e ..2....2....3....3....3....3....3....2....3....3

%e ..3....3....3....3....3....3....3....3....3....3

%Y Cf. A190041.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 04 2011