login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A016778 a(n) = (3*n+1)^2. 12
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 (list; graph; refs; listen; history; text; internal format)
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

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

CROSSREFS

Cf. A016777, A016779, A016780, A016781, A214550.

Cf. A000212, A214550, A262178.

Sequence in context: A329075 A041496 A059207 * A009952 A105823 A112630

Adjacent sequences:  A016775 A016776 A016777 * A016779 A016780 A016781

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 28 21:56 EST 2020. Contains 338755 sequences. (Running on oeis4.)