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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. 2
1, 5, 24, 115, 550, 2631, 12584, 60191, 287901, 1377066, 6586677, 31504891, 150691790, 720777469, 3447567781, 16490143094, 78874393932, 377265981421, 1804509849677, 8631193794141, 41284067429916, 197466800561799, 944508129929499, 4517699202928696 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 11 07:29 EST 2019. Contains 329914 sequences. (Running on oeis4.)