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A010015 a(0) = 1, a(n) = 25*n^2 + 2 for n > 0. 1
1, 27, 102, 227, 402, 627, 902, 1227, 1602, 2027, 2502, 3027, 3602, 4227, 4902, 5627, 6402, 7227, 8102, 9027, 10002, 11027, 12102, 13227, 14402, 15627, 16902, 18227, 19602, 21027, 22502, 24027, 25602, 27227, 28902, 30627, 32402, 34227, 36102, 38027, 40002 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Subsequence of A160842. - Bruno Berselli, Feb 06 2012

The identity (25*n^2 + 1)^2 - (25*n^2 + 2)*(5*n)^2 = 1 can be written as (A016850(n+1) + 1)^2 - a(n+1)*A008587(n+1)^2 = 1. - Vincenzo Librandi, Feb 08 2012

LINKS

Bruno Berselli, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f.: (1+x)*(1 + 23*x + x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012

E.g.f.: (x*(x+1)*25 + 2)*e^x - 1. - Gopinath A. R., Feb 14 2012

MATHEMATICA

Join[{1}, 25 Range[40]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)

Join[{1}, LinearRecurrence[{3, -3, 1}, {27, 102, 227}, 50]] (* Vincenzo Librandi, Feb 08 2012 *)

PROG

(PARI) A010015(n)=25*n^2+2-!n \\ M. F. Hasler, Feb 14 2012

CROSSREFS

Cf. A206399.

Sequence in context: A118615 A197619 A033659 * A256646 A323034 A031429

Adjacent sequences:  A010012 A010013 A010014 * A010016 A010017 A010018

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 18 18:06 EDT 2021. Contains 345120 sequences. (Running on oeis4.)