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A001539 (4n+1)(4n+3). 12
3, 35, 99, 195, 323, 483, 675, 899, 1155, 1443, 1763, 2115, 2499, 2915, 3363, 3843, 4355, 4899, 5475, 6083, 6723, 7395, 8099, 8835, 9603, 10403, 11235, 12099, 12995, 13923, 14883, 15875, 16899, 17955, 19043, 20163, 21315, 22499, 23715, 24963, 26243, 27555 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Sequence arises from reading the line from 3, in the direction 3, 35,... in the square spiral whose vertices are the squares A000290. - Omar E. Pol, May 24 2008

(log(sq(2)+1))/sqrt(2) = .62322524...= 2/3 - 2/35 + 2/99 - 2/195 + 2/323,...; = (1 - 1/3) + (1/7 - 1/5) + (1/9 - 1/11) + (1/15 - 1/13) + (1/17 - 1/19) + (1/23 - 1/21) + ... [From Gary W. Adamson, Mar 01 2009]

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

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

FORMULA

Sum(k>=0, 1/a(k)) = Pi/8 - Benoit Cloitre, Aug 20 2002

G.f.: (3+26*x+3*x^2)/(1-x)^3 [From Jaume Oliver Lafont, Mar 07 2009]

a(n)=32*n+a(n-1), with a(0)=3 [From Vincenzo Librandi,

PROG

(Maxima) A001539(n):=(4*n+1)*(4*n+3)$

makelist(A001539(n), n, 0, 30); /* Martin Ettl, Nov 12 2012 */

CROSSREFS

a(n) = A016826(n) - 1 = [A001533(n)+5]/4 = [A001538(n)+16]/9.

Bisection of A000466.

Cf. A000290, A016286.

Cf. A157142, A133766, A154633.

Sequence in context: A054287 A176761 A246824 * A113854 A231645 A076376

Adjacent sequences:  A001536 A001537 A001538 * A001540 A001541 A001542

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 21 06:19 EST 2014. Contains 252297 sequences.