

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
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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 semiaxis 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+(449120*sqrt(14))^n2).  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)/(1x)^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



