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
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Oct 13 2011
STATUS
approved