

A195024


a(n) = n*(14*n  1).


10



0, 13, 54, 123, 220, 345, 498, 679, 888, 1125, 1390, 1683, 2004, 2353, 2730, 3135, 3568, 4029, 4518, 5035, 5580, 6153, 6754, 7383, 8040, 8725, 9438, 10179, 10948, 11745, 12570, 13423, 14304, 15213, 16150, 17115, 18108, 19129, 20178, 21255, 22360
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OFFSET

0,2


COMMENTS

Related to the primitive Pythagorean triple [3, 4, 5].
Sequence found by reading the line from 0, in the direction 0, 13, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. This is the one of the semidiagonals of the square spiral.
Also sequence found by reading the line from 0, in the direction 0, 13, ..., in the square spiral whose vertices are the generalized 9gonal numbers A118277.  Omar E. Pol, Jul 28 2012


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  n.
From Colin Barker, Apr 09 2012: (Start)
a(n) = 3*a(n1)  3*a(n2) + a(n3).
G.f.: x*(13+15*x)/(1x)^3. (End)


MATHEMATICA

Table[n(14n1), {n, 0, 50}] (* or *) LinearRecurrence[{3, 3, 1}, {0, 13, 54}, 50] (* Harvey P. Dale, Jul 28 2012 *)


PROG

(MAGMA) [14*n^2  n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011
(PARI) a(n)=n*(14*n1) \\ Charles R Greathouse IV, Oct 07 2015


CROSSREFS

Cf. A144555, A152760, A195019, A195020, A195320, A185019, A193053, A198017.
Sequence in context: A201486 A176617 A254895 * A071230 A027000 A198160
Adjacent sequences: A195021 A195022 A195023 * A195025 A195026 A195027


KEYWORD

nonn,easy


AUTHOR

Omar E. Pol, Oct 13 2011


STATUS

approved



