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

Author

Alois P. Heinz, May 19 2014

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7, 21, 60, 128, 253, 444, 740, 1145, 1700, 2398, 3266, 4267, 5412, 6627, 7896, 9123, 10275, 11246, 12016, 12491, 12681, 12534, 12099, 11364, 10420, 9287, 8069, 6801, 5578, 4420, 3400, 2512, 1792, 1217, 793, 482, 278, 144, 69, 26, 9).

Crossrefs

Column k=10 of A242464.

Programs

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);

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).