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A185212 a(n) = 12*n^2 - 8*n + 1. 3
1, 5, 33, 85, 161, 261, 385, 533, 705, 901, 1121, 1365, 1633, 1925, 2241, 2581, 2945, 3333, 3745, 4181, 4641, 5125, 5633, 6165, 6721, 7301, 7905, 8533, 9185, 9861, 10561, 11285, 12033, 12805, 13601, 14421, 15265, 16133, 17025, 17941, 18881, 19845, 20833 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sequence found by reading the line from 1, in the direction 1, 5, and the same line from 5, in the direction 5, 33, ..., in the square spiral whose vertices are the generalized octagonal numbers A001082. - Omar E. Pol, May 08 2018

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = 4*A000567(n) + 1.

a(0)=1, a(1)=5, a(2)=33, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Jul 07 2015

G.f.: (-1-2*x-21*x^2)/(-1+x)^3. - Harvey P. Dale, Jul 07 2015

E.g.f.: (12*x^2 + 4*x + 1)*exp(x). - G. C. Greubel, Jun 25 2017

MATHEMATICA

Table[12n^2-8n+1, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 5, 33}, 50] (* Harvey P. Dale, Jul 07 2015 *)

PROG

(Haskell)

a185212 = (+ 1) . (* 4) . a000567

(PARI) a(n)=12*n^2-8*n+1 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

For n > 0: odd terms in A001859.

Cf. A001082.

Sequence in context: A194405 A299518 A135111 * A250225 A250273 A050830

Adjacent sequences:  A185209 A185210 A185211 * A185213 A185214 A185215

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Dec 20 2012

STATUS

approved

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Last modified February 22 15:26 EST 2020. Contains 332137 sequences. (Running on oeis4.)