A168235 1+5*n+7*n^2.

13, 39, 79, 133, 201, 283, 379, 489, 613, 751, 903, 1069, 1249, 1443, 1651, 1873, 2109, 2359, 2623, 2901, 3193, 3499, 3819, 4153, 4501, 4863, 5239, 5629, 6033, 6451, 6883, 7329, 7789, 8263, 8751, 9253, 9769, 10299, 10843, 11401, 11973, 12559, 13159, 13773

Offset

1,1

Comments

Consider the quadratic cyclotomic polynomial f(x) = x^2+x+1 and the quotients defined by f(x + n*f(x))/f(x). a(n) is the quotient at x=2.

See A168240 for x=3 or A168244 for x= 1+sqrt(-5).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(1)=13, a(2)=39, a(3)=79, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Feb 07 2015

From G. C. Greubel, Apr 09 2016: (Start)

G.f.: (1 + 10*x + 3*x^2)/(1-x)^3.

E.g.f.: (1 + 12*x + 7*x^2)*exp(x). (End)

Example

When x = 2, f(x) = 7. Hence at n=1, f( x + f(x))/f(x) = 13 = a(1).

Mathematica

Table[1+5n+7n^2, {n, 60}] (* or *) LinearRecurrence[{3, -3, 1}, {13, 39, 79}, 60] (* Harvey P. Dale, Feb 07 2015 *)

Prog

(PARI) a(n)=1+5*n+7*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A165806, A165808, A165809.

Sequence in context: A158647 A283123 A152741 * A258597 A299816 A041324

Adjacent sequences: A168232 A168233 A168234 * A168236 A168237 A168238

Keyword

nonn,easy

Author

A.K. Devaraj, Nov 21 2009

Extensions

Edited, definition simplified, sequence extended beyond a(8) by R. J. Mathar, Nov 23 2009

Status

approved