login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A010008 a(0) = 1, a(n) = 18*n^2 + 2 for n>0. 2
1, 20, 74, 164, 290, 452, 650, 884, 1154, 1460, 1802, 2180, 2594, 3044, 3530, 4052, 4610, 5204, 5834, 6500, 7202, 7940, 8714, 9524, 10370, 11252, 12170, 13124, 14114, 15140, 16202, 17300, 18434, 19604, 20810, 22052, 23330, 24644, 25994, 27380, 28802, 30260 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The identity (18*n^2+2)^2-(9*n^2+2)*(6*n)^2=4 can be written as a(n+1)^2-A010002(n+1)*A008588(n+1)^2=4. - Vincenzo Librandi, Feb 07 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+16*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012

a(n) = (3*n-1)^2+(3*n+1)^2 = (n-1)^2+(n+1)^2+(4*n)^2 for n>0. - Bruno Berselli, Feb 06 2012

E.g.f.: (x*(x+1)*18+2)*e^x-1. - Gopinath A. R., Feb 14 2012

MATHEMATICA

Join[{1}, 18 Range[41]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)

Join[{1}, LinearRecurrence[{3, -3, 1}, {20, 74, 164}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)

PROG

(MAGMA) [1] cat [18*n^2+2: n in [1..50]]; // Vincenzo Librandi, Aug 03 2015

CROSSREFS

After 20, all terms are in A000408.

Cf. A206399.

Sequence in context: A002292 A225923 A238026 * A237617 A000529 A238027

Adjacent sequences:  A010005 A010006 A010007 * A010009 A010010 A010011

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Bruno Berselli, Feb 06 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 10:48 EDT 2019. Contains 323529 sequences. (Running on oeis4.)