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A158482 14n^2 + 1. 5
15, 57, 127, 225, 351, 505, 687, 897, 1135, 1401, 1695, 2017, 2367, 2745, 3151, 3585, 4047, 4537, 5055, 5601, 6175, 6777, 7407, 8065, 8751, 9465, 10207, 10977, 11775, 12601, 13455, 14337, 15247, 16185, 17151, 18145, 19167, 20217, 21295, 22401 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (14*n^2+1)^2-(49*n^2+7)*(2*n)^2=1 can be written as a(n)^2-A158481(n)*A005843(n)^2=1.

Sequence found by reading the line from 15, in the direction 15, 57,..., in the square spiral whose vertices are the generalized enneagonal numbers  numbers A118277. Also sequence found by reading the same line in the square spiral whose edges have length A195019 and whose vertices are the numbers A195020. - Omar E. Pol, Sep 13 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

FORMULA

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

G.f: x*(15+12*x+x^2)/(1-x)^3.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {15, 57, 127}, 50]

PROG

(MAGMA) I:=[15, 57, 127]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];

(PARI) a(n) = 14*n^2+1;

CROSSREFS

Cf. A005843, A158481.

Sequence in context: A140379 A020222 A256867 * A184223 A084815 A240152

Adjacent sequences:  A158479 A158480 A158481 * A158483 A158484 A158485

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 20 2009

STATUS

approved

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Last modified October 15 22:21 EDT 2018. Contains 316252 sequences. (Running on oeis4.)