OFFSET
0,2
COMMENTS
From Paul Curtz, Mar 28 2019: (Start)
Sequence is a spoke of the hexagonal spiral built from the terms of A016777:
.
\
100--97--94--91
\ \
49--46--43 88
/ \ \ \
52 16--13 40 85
/ / \ \ \ \
55 19 1 10 37 82
/ / / / / /
58 22 4---7 34 79
\ \ / /
61 25--28--31 76
\ /
64--67--70--73
(End)
LINKS
Shawn A. Broyles, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = a(n-1) + 3*(6*n-1); a(0)=1. - Vincenzo Librandi, Nov 20 2010
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=1, a(1)=16, a(2)=49. - Harvey P. Dale, Mar 03 2013
a(n) = A247792(n) + 6*n. - Miquel Cerda, Oct 23 2016
G.f.: (1 + 13*x + 4*x^2)/(1 - x)^3. - Ilya Gutkovskiy, Oct 23 2016
From Amiram Eldar, Nov 12 2020: (Start)
Sum_{n>=0} 1/a(n) = A214550.
Sum_{n>=0} (-1)^n/a(n) = A262178. (End)
MATHEMATICA
(3*Range[0, 50]+1)^2 (* or *) LinearRecurrence[{3, -3, 1}, {1, 16, 49}, 50] (* Harvey P. Dale, Mar 03 2013 *)
PROG
(Maxima) A016778(n):=(3*n+1)^2$
makelist(A016778(n), n, 0, 20); /* Martin Ettl, Nov 12 2012 */
(PARI) a(n)=(3*n+1)^2 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved