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A156814
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a(n) = 225*n^2 + n.
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3
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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
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OFFSET
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1,1
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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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
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {226, 902, 2028}, 50] (* Vincenzo Librandi, Feb 08 2012 *)
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PROG
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(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
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CROSSREFS
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Cf. A156840.
Sequence in context: A218040 A158229 A031708 * A251605 A233943 A234155
Adjacent sequences: A156811 A156812 A156813 * A156815 A156816 A156817
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Feb 16 2009
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STATUS
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approved
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