login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195025 a(n) = n*(14*n + 3). 7
0, 17, 62, 135, 236, 365, 522, 707, 920, 1161, 1430, 1727, 2052, 2405, 2786, 3195, 3632, 4097, 4590, 5111, 5660, 6237, 6842, 7475, 8136, 8825, 9542, 10287, 11060, 11861, 12690, 13547, 14432, 15345, 16286, 17255, 18252, 19277, 20330, 21411, 22520 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sequence found by reading the line from 0, in the direction 0, 17, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. This is the one of the semi-axis of the square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].

a(k) is a square for k=(3/56)*((449+120*sqrt(14))^n+(449-120*sqrt(14))^n-2). - Bruno Berselli, Oct 18 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

FORMULA

a(n) =  14*n^2 + 3*n.

G.f.: x*(17+11*x)/(1-x)^3. - Bruno Berselli, Oct 18 2011

PROG

(MAGMA) [14*n^2 +3*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011

(PARI) a(n)=n*(14*n+3) \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A144555, A152760, A185019, A195019, A195020, A195023, A195024, A193053, A195320.

Sequence in context: A211593 A211587 A226026 * A010005 A172076 A063522

Adjacent sequences:  A195022 A195023 A195024 * A195026 A195027 A195028

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Oct 13 2011

EXTENSIONS

Name suggested by Bruno Berselli, Oct 13 2011

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 July 31 04:27 EDT 2021. Contains 346367 sequences. (Running on oeis4.)