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

0,2

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).

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).

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 *)

Crossrefs

Cf. A242452, A242495.

Sequence in context: A289783 A140766 A026388 * A057969 A004254 A086347

Adjacent sequences: A242506 A242507 A242508 * A242510 A242511 A242512

Keyword

nonn,easy

Author

Geoffrey Critzer and Alois P. Heinz, May 16 2014

Status

approved