cp's OEIS Frontend

A269438 Number of length-6 0..n arrays with no repeated value greater than the previous repeated value.

%I A269438 #8 Jan 22 2019 07:44:37
%S A269438 51,622,3674,14455,44021,112476,252932,516189,976135,1735866,2934526,
%T A269438 4754867,7431529,11260040,16606536,23918201,33734427,46698694,
%U A269438 63571170,85242031,112745501,147274612,190196684,243069525,307658351,385953426
%N A269438 Number of length-6 0..n arrays with no repeated value greater than the previous repeated value.
%H A269438 R. H. Hardin, <a href="/A269438/b269438.txt">Table of n, a(n) for n = 1..210</a>
%F A269438 Empirical: a(n) = n^6 + 6*n^5 + 12*n^4 + (44/3)*n^3 + (23/2)*n^2 + (29/6)*n + 1.
%F A269438 Conjectures from _Colin Barker_, Jan 22 2019: (Start)
%F A269438 G.f.: x*(51 + 265*x + 391*x^2 + 14*x^3 + 5*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F A269438 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A269438 (End)
%e A269438 Some solutions for n=6:
%e A269438 ..0. .0. .0. .0. .1. .5. .6. .4. .4. .1. .2. .3. .5. .2. .4. .5
%e A269438 ..5. .4. .1. .3. .5. .4. .2. .2. .3. .2. .4. .2. .1. .0. .2. .5
%e A269438 ..4. .6. .4. .5. .0. .6. .2. .5. .1. .5. .3. .6. .5. .2. .1. .2
%e A269438 ..5. .5. .4. .0. .5. .5. .2. .3. .4. .5. .4. .5. .5. .4. .2. .6
%e A269438 ..3. .3. .6. .2. .0. .0. .0. .0. .1. .5. .1. .5. .2. .1. .5. .2
%e A269438 ..3. .3. .3. .4. .5. .2. .3. .0. .4. .3. .6. .5. .0. .6. .2. .4
%Y A269438 Row 6 of A269435.
%K A269438 nonn
%O A269438 1,1
%A A269438 _R. H. Hardin_, Feb 26 2016