A242630 Number of n-length words w over a 7-ary alphabet {a_1,...,a_7} such that w contains never more than j consecutive letters a_j (for 1<=j<=7).

1, 7, 48, 329, 2254, 15443, 105804, 724892, 4966431, 34026362, 233123809, 1597194268, 10942809918, 74972150416, 513654479985, 3519185768909, 24110893526041, 165190252745398, 1131763100053353, 7754015102916294, 53124854674462893, 363972747889200054

Offset

0,2

Links

Geoffrey Critzer and Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: -(x+1) *(x^2+1) *(x^4+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(x^2+x+1) *(x^2-x+1) *(x^4+x^3+x^2+x+1) / (6*x^21 +17*x^20 +39*x^19 +70*x^18 +117*x^17 +170*x^16 +233*x^15 +289*x^14 +340*x^13 +369*x^12 +382*x^11 +364*x^10 +331*x^9 +277*x^8 +220*x^7 +157*x^6 +106*x^5 +61*x^4 +33*x^3 +13*x^2 +4*x-1).

Crossrefs

Column k=7 of A242464.

Sequence in context: A289785 A036829 A164591 * A004187 A180167 A341425

Adjacent sequences: A242627 A242628 A242629 * A242631 A242632 A242633

Keyword

nonn,easy

Author

Geoffrey Critzer and Alois P. Heinz, May 19 2014

Status

approved