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

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).

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