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.

1, 5, 24, 115, 550, 2631, 12584, 60191, 287901, 1377066, 6586677, 31504891, 150691790, 720777469, 3447567781, 16490143094, 78874393932, 377265981421, 1804509849677, 8631193794141, 41284067429916, 197466800561799, 944508129929499, 4517699202928696

Offset: 0

Author

Geoffrey Critzer and Alois P. Heinz, May 16 2014

Keywords

• nonn
• easy

Comments

Column k=5 of A242464.

Links

• Fung Lam, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3, 5, 12, 17, 24, 24, 25, 19, 14, 7, 4).

Crossrefs

Cf. A242452, A242495.

Programs

Mathematica

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]
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 *)

Formula

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).