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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
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
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: A341085 A301858 A293174 * A097812 A176333 A100559
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