A195024 a(n) = n*(14*n - 1).

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

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 semi-diagonals 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 9-gonal 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(n-1) - 3*a(n-2) + a(n-3).

G.f.: x*(13+15*x)/(1-x)^3. (End)

Mathematica

Table[n(14n-1), {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*n-1) \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A144555, A152760, A195019, A195020, A195320, A185019, A193053, A198017.

Sequence in context: A176617 A254895 A358166 * A071230 A027000 A198160

Adjacent sequences: A195021 A195022 A195023 * A195025 A195026 A195027

Keyword

nonn,easy

Author

Omar E. Pol, Oct 13 2011

Status

approved