A156814 a(n) = 225*n^2 + n.

226, 902, 2028, 3604, 5630, 8106, 11032, 14408, 18234, 22510, 27236, 32412, 38038, 44114, 50640, 57616, 65042, 72918, 81244, 90020, 99246, 108922, 119048, 129624, 140650, 152126, 164052, 176428, 189254, 202530, 216256, 230432, 245058, 260134

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

Formula

From Vincenzo Librandi, Feb 08 2012: (Start)

900*a(n) + 1 = (450*n + 1)^2.

G.f.: 2*x*(113 + 112*x)/(1-x)^3.

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

E.g.f.: x*(226 + 225*x)*exp(x). - G. C. Greubel, Jun 10 2021

Mathematica

LinearRecurrence[{3, -3, 1}, {226, 902, 2028}, 50] (* Vincenzo Librandi, Feb 08 2012 *)

Prog

(PARI) a(n)=225*n^2+n \\ Charles R Greathouse IV, Dec 23 2011
(Magma) I:=[226, 902, 2028]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 08 2012
(Sage) [n*(1+225*n) for n in [1..50]] # G. C. Greubel, Jun 10 2021

Crossrefs

Cf. A156840.

Sequence in context: A218040 A158229 A031708 * A251605 A233943 A234155

Adjacent sequences: A156811 A156812 A156813 * A156815 A156816 A156817

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 16 2009

Status

approved