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A181890 8n^2 + 14n + 5. 7
5, 27, 65, 119, 189, 275, 377, 495, 629, 779, 945, 1127, 1325, 1539, 1769, 2015, 2277, 2555, 2849, 3159, 3485, 3827, 4185, 4559, 4949, 5355, 5777, 6215, 6669, 7139, 7625, 8127, 8645, 9179, 9729, 10295, 10877 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A160050(4*n+1) = A033954(n); A160050(4*n+2) = A001107(n); the third quadrisection is a(n).

First 16 terms of clockwise spiral for odd numbers is

13 15 17 19

11  1  3 21

09  7  5 23

31 29 27 25

a(n) comes from the third vertical.

Sequence found by reading the line from 5, in the direction 5, 27, in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Dec 25 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = A160050(4*n+3).

a(n) = (2*n+1)*(4*n+5).

a(n) = a(n-1)+16*n+6;

a(n) = 2*a(n-1)-a(n-2)+16.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3).

G.f.: (5 + 12*x - x^2)/(1 - x)^3. [Arkadiusz Wesolowski, Dec 25 2011]

a(n) = A014635(n+1) - 1. - Omar E. Pol, Dec 25 2011

MATHEMATICA

Table[(2n+1)(4n+5), {n, 0, 40}]  (* Harvey P. Dale, Feb 06 2011 *)

CoefficientList[Series[(5 + 12 x - x^2)/(1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, May 23 2014 *)

PROG

(MAGMA) [8*n^2+14*n+5: n in [0..700]]; // Vincenzo Librandi, Feb 01 2011

(PARI) a(n)=8*n^2+14*n+5 \\ Charles R Greathouse IV, Dec 21 2011

CROSSREFS

Cf. A000217, A014635, A064038, A160050.

Sequence in context: A156215 A058490 A136917 * A048712 A121876 A137116

Adjacent sequences:  A181887 A181888 A181889 * A181891 A181892 A181893

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Feb 01 2011

STATUS

approved

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Last modified September 22 09:19 EDT 2017. Contains 292336 sequences.