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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).

%I A242633 #9 Aug 17 2024 11:13:30
%S A242633 1,10,99,980,9700,96011,950319,9406280,93103581,921541438,9121438862,
%T A242633 90284216730,893635304019,8845223290551,87550228496839,
%U A242633 866574224082841,8577372083864876,84899030943287514,840332608243515705,8317631952113371291,82328117000511661919
%N 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).
%H A242633 Alois P. Heinz, <a href="/A242633/b242633.txt">Table of n, a(n) for n = 0..1000</a>
%H A242633 <a href="/index/Rec#order_41">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A242633 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).
%p A242633 b:= proc(n, k, c, t) option remember;
%p A242633       `if`(n=0, 1, add(`if`(c=t and j=c, 0,
%p A242633        b(n-1, k, j, 1+`if`(j=c, t, 0))), j=1..k))
%p A242633     end:
%p A242633 a:= n-> b(n, 10, 0$2):
%p A242633 seq(a(n), n=0..30);
%Y A242633 Column k=10 of A242464.
%K A242633 nonn,easy
%O A242633 0,2
%A A242633 _Alois P. Heinz_, May 19 2014