A082804 - OEIS

%I #14 Mar 23 2017 04:51:50

%S 18,27,36,45,54,63,72,81,9,108,117,126,135,144,153,162,171,18,198,207,

%T 216,225,234,243,252,261,27,288,297,306,315,324,333,342,351,36,378,

%U 387,396,405,414,423,432,441,45,468,477,486,495,504,513,522,531,54,558,567

%N Smallest multiple of 9 beginning with n.

%H Vincenzo Librandi, <a href="/A082804/b082804.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,-1).

%F From _Colin Barker_, Mar 23 2017: (Start)

%F G.f.: 9*x*(2 + 3*x + 4*x^2 + 5*x^3 + 6*x^4 + 7*x^5 + 8*x^6 + 9*x^7 + x^8 + 8*x^9 + 7*x^10 + 6*x^11 + 5*x^12 + 4*x^13 + 3*x^14 + 2*x^15 + x^16) / ((1 - x)^2*(1 + x + x^2)^2*(1 + x^3 + x^6)^2).

%F a(n) = 2*a(n-9) - a(n-18) for n>17.

%F (End)

%t Table[If[Mod[n,9]==0,n,10n+9-Mod[n,9]],{n,56}] (* _Ray Chandler_, Feb 09 2014 *)

%o (PARI) Vec(9*x*(2 + 3*x + 4*x^2 + 5*x^3 + 6*x^4 + 7*x^5 + 8*x^6 + 9*x^7 + x^8 + 8*x^9 + 7*x^10 + 6*x^11 + 5*x^12 + 4*x^13 + 3*x^14 + 2*x^15 + x^16) / ((1 - x)^2*(1 + x + x^2)^2*(1 + x^3 + x^6)^2) + O(x^60)) \\ _Colin Barker_, Mar 23 2017

%Y Cf. A082799, A082800, A082801, A082802, A082803.

%K nonn,base,easy

%O 1,1

%A _Amarnath Murthy_, Apr 20 2003

%E Extended by _Ray Chandler_, Feb 09 2014