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 A108928 a(n) = 8*n^2 - 3. 3
 5, 29, 69, 125, 197, 285, 389, 509, 645, 797, 965, 1149, 1349, 1565, 1797, 2045, 2309, 2589, 2885, 3197, 3525, 3869, 4229, 4605, 4997, 5405, 5829, 6269, 6725, 7197, 7685, 8189, 8709, 9245, 9797, 10365, 10949, 11549, 12165, 12797, 13445, 14109, 14789 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sequence found by reading the segment (5, 29) together with the line from 29, in the direction 29, 69,..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 04 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) = 2*(2*n-1)*(2*n+1)-1. a(1)=5, a(2)=29, a(3)=69, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Jul 21 2012 From G. C. Greubel, Jul 15 2017:(Start) G.f.: x*(-5 - 14*x + 3*x^2)/(-1 + x)^3. E.g.f.: (8*x^2 + 8*x - 3)*exp(x) + 3. (End) EXAMPLE (1*3 = 3)+2 = 5; (3*5 = 15)+14 = 29; (5*7 = 35)+34 = 69; (7*9 = 63)+62 = 125; ... MAPLE seq(8*n^2-3, n=1..50); # Emeric Deutsch, Aug 01 2005 MATHEMATICA 8*Range[50]^2-3 (* or *) LinearRecurrence[{3, -3, 1}, {5, 29, 69}, 50] (* Harvey P. Dale, Jul 21 2012 *) PROG (PARI) a(n)=8*n^2-3 \\ Charles R Greathouse IV, Sep 04 2011 (MAGMA) [8*n^2 - 3: n in [1..50]]; // Vincenzo Librandi, Sep 05 2011 CROSSREFS Sequence in context: A103094 A301858 A293174 * A097812 A176333 A100559 Adjacent sequences:  A108925 A108926 A108927 * A108929 A108930 A108931 KEYWORD easy,nonn AUTHOR Marcel Hetkowski Fabeny (marcelfabeny(AT)yahoo.com.br), Jul 19 2005 EXTENSIONS More terms from Emeric Deutsch, Aug 01 2005 STATUS approved

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Last modified August 8 08:27 EDT 2020. Contains 336293 sequences. (Running on oeis4.)