A168418 a(n) = 9*n - a(n-1) - 8 with n>1, a(1)=5.

5, 5, 14, 14, 23, 23, 32, 32, 41, 41, 50, 50, 59, 59, 68, 68, 77, 77, 86, 86, 95, 95, 104, 104, 113, 113, 122, 122, 131, 131, 140, 140, 149, 149, 158, 158, 167, 167, 176, 176, 185, 185, 194, 194, 203, 203, 212, 212, 221, 221, 230, 230, 239, 239, 248, 248, 257

Offset

1,1

Links

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

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

Formula

From R. J. Mathar, Jan 26 2010: (Start)

a(n) = A168213(n-1), n>1.

G.f.: x*(5 + 4*x^2)/((1+x)*(x-1)^2). (End)

From G. C. Greubel, Jul 22 2016: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3).

E.g.f.: (1/4)*(-9 + 16*exp(x) + (18*x - 7)*exp(2*x))*exp(-x). (End)

Mathematica

LinearRecurrence[{1, 1, -1}, {5, 5, 14}, 60] (* Vincenzo Librandi, Feb 27 2012 *)
RecurrenceTable[{a[1]==5, a[n]==9n-a[n-1]-8}, a, {n, 60}] (* or *) With[ {c= LinearRecurrence[{2, -1}, {5, 14}, 40]}, Riffle[c, c]] (* or *) With[{c= 9* Range[ 40]-4}, Riffle[c, c]] (* Harvey P. Dale, Jan 25 2019 *)

Prog

(Magma) I:=[5, 5, 14]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // Vincenzo Librandi, Feb 28 2012

Crossrefs

Sequence in context: A252768 A062367 A286257 * A266440 A317617 A294750

Adjacent sequences: A168415 A168416 A168417 * A168419 A168420 A168421

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 25 2009

Status

approved