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A016778
a(n) = (3*n+1)^2.
29
1, 16, 49, 100, 169, 256, 361, 484, 625, 784, 961, 1156, 1369, 1600, 1849, 2116, 2401, 2704, 3025, 3364, 3721, 4096, 4489, 4900, 5329, 5776, 6241, 6724, 7225, 7744, 8281, 8836, 9409, 10000, 10609, 11236
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)
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
a(n) = A000212(3*n) + A000212(1+3*n) + A000212(2+3*n). - Paul Curtz, Mar 28 2019
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
KEYWORD
nonn,easy
STATUS
approved