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A242509 Number of n-length words on {1,2,3,4,5} that contain at most one consecutive 1 and at most two consecutive 2's and at most three consecutive 3's and at most four consecutive 4's and at most five consecutive 5's.

%I A242509 #33 Apr 13 2019 17:37:54
%S A242509 1,5,24,115,550,2631,12584,60191,287901,1377066,6586677,31504891,
%T A242509 150691790,720777469,3447567781,16490143094,78874393932,377265981421,
%U A242509 1804509849677,8631193794141,41284067429916,197466800561799,944508129929499,4517699202928696
%N A242509 Number of n-length words on {1,2,3,4,5} that contain at most one consecutive 1 and at most two consecutive 2's and at most three consecutive 3's and at most four consecutive 4's and at most five consecutive 5's.
%C A242509 Column k=5 of A242464.
%H A242509 Fung Lam, <a href="/A242509/b242509.txt">Table of n, a(n) for n = 0..1000</a>
%H A242509 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3, 5, 12, 17, 24, 24, 25, 19, 14, 7, 4).
%F A242509 G.f.: (1 + x)*(1 +x^2)*(1 - x + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)/(1 - 3*x - 5*x^2 - 12*x^3 - 17*x^4 - 24*x^5 - 24*x^6 - 25*x^7 - 19*x^8 - 14*x^9 - 7*x^10 - 4*x^11).
%t A242509 nn=23;CoefficientList[Series[1/(1-Sum[v[i]/(1+v[i])/.v[i]->(z-z^(i+1))/(1-z),{i,1,5}]),{z,0,nn}],z]
%t A242509 LinearRecurrence[{3,5,12,17,24,24,25,19,14,7,4},{1,5,24,115,550,2631,12584,60191,287901,1377066,6586677,31504891},30] (* _Harvey P. Dale_, Apr 13 2019 *)
%Y A242509 Cf. A242452, A242495.
%K A242509 nonn,easy
%O A242509 0,2
%A A242509 _Geoffrey Critzer_ and _Alois P. Heinz_, May 16 2014