



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
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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(n1)3*a(n2)+a(n3).  Harvey P. Dale, Feb 07 2015
From G. C. Greubel, Apr 09 2016: (Start)
G.f.: (1 + 10*x + 3*x^2)/(1x)^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



