A242633 Number of n-length words w over a 10-ary alphabet {a_1,...,a_10} such that w contains never more than j consecutive letters a_j (for 1<=j<=10).

1, 10, 99, 980, 9700, 96011, 950319, 9406280, 93103581, 921541438, 9121438862, 90284216730, 893635304019, 8845223290551, 87550228496839, 866574224082841, 8577372083864876, 84899030943287514, 840332608243515705, 8317631952113371291, 82328117000511661919

Offset

0,2

Links

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

Formula

G.f.: -(x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) *(x+1)*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1) *(x^2+x+1) *(x^6+x^3+1) *(x^2+1) *(x^4+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(x^2-x+1) / (9*x^41 +26*x^40 +69*x^39 +144*x^38 +278*x^37 +482*x^36 +793*x^35 +1217*x^34 +1792*x^33 +2512*x^32 +3400*x^31 +4420*x^30 +5578*x^29 +6801*x^28 +8069*x^27 +9287*x^26 +10420*x^25 +11364*x^24 +12099*x^23 +12534*x^22 +12681*x^21 +12491*x^20 +12016*x^19 +11246*x^18 +10275*x^17 +9123*x^16 +7896*x^15 +6627*x^14 +5412*x^13 +4267*x^12 +3266*x^11 +2398*x^10 +1700*x^9 +1145*x^8 +740*x^7 +444*x^6 +253*x^5 +128*x^4 +60*x^3 +21*x^2 +7*x-1).

Maple

b:= proc(n, k, c, t) option remember;
      `if`(n=0, 1, add(`if`(c=t and j=c, 0,
       b(n-1, k, j, 1+`if`(j=c, t, 0))), j=1..k))
    end:
a:= n-> b(n, 10, 0$2):
seq(a(n), n=0..30);

Crossrefs

Column k=10 of A242464.

Sequence in context: A171315 A370043 A081109 * A004189 A322054 A179558

Adjacent sequences: A242630 A242631 A242632 * A242634 A242635 A242636

Keyword

nonn,easy

Author

Alois P. Heinz, May 19 2014

Status

approved