A082804 Smallest multiple of 9 beginning with n.

18, 27, 36, 45, 54, 63, 72, 81, 9, 108, 117, 126, 135, 144, 153, 162, 171, 18, 198, 207, 216, 225, 234, 243, 252, 261, 27, 288, 297, 306, 315, 324, 333, 342, 351, 36, 378, 387, 396, 405, 414, 423, 432, 441, 45, 468, 477, 486, 495, 504, 513, 522, 531, 54, 558, 567

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,-1).

Formula

From Colin Barker, Mar 23 2017: (Start)

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).

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

(End)

Mathematica

Table[If[Mod[n, 9]==0, n, 10n+9-Mod[n, 9]], {n, 56}] (* Ray Chandler, Feb 09 2014 *)

Prog

(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

Crossrefs

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

Sequence in context: A265738 A151741 A090064 * A262277 A144777 A296130

Adjacent sequences: A082801 A082802 A082803 * A082805 A082806 A082807

Keyword

nonn,base,easy

Author

Amarnath Murthy, Apr 20 2003

Extensions

Extended by Ray Chandler, Feb 09 2014

Status

approved