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A016778 a(n) = (3*n+1)^2. 11
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

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.

Sequence in context: A231526 A041496 A059207 * A009952 A105823 A112630

Adjacent sequences:  A016775 A016776 A016777 * A016779 A016780 A016781

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 20 22:22 EDT 2019. Contains 322310 sequences. (Running on oeis4.)