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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).
2
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
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
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, May 19 2014
STATUS
approved