



5, 4, 1, 4, 11, 20, 31, 44, 59, 76, 95, 116, 139, 164, 191, 220, 251, 284, 319, 356, 395, 436, 479, 524, 571, 620, 671, 724, 779, 836, 895, 956, 1019, 1084, 1151, 1220, 1291, 1364, 1439, 1516, 1595, 1676, 1759, 1844, 1931, 2020, 2111, 2204, 2299, 2396
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OFFSET

0,1


COMMENTS

a(n) gives the values for a*c of indefinite binary quadratic forms [a, b, c] of discriminant D = 20 for b = 2*n. In general D = b^2  4*a*c > 0 and the form [a, b, c] is a*x^2 + b*x*y + c*y^2.  Wolfdieter Lang, Aug 15 2013
For n>2, a(n) represents the area of the triangle created by the three points defined with coordinates: (n3,n2), ((n1)*n/2,n*(n+1)/2), and ((n+1)^2, (n+2)^2).  J. M. Bergot, May 22 2014


LINKS

Table of n, a(n) for n=0..49.
Eric Weisstein's World of Mathematics, NearSquare Prime
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

G.f.: x^3*(4+x+x^2)/(1+x)^3. a(n) = 3a(n1)  3a(n2) + a(n3).  R. J. Mathar, Apr 28 2008
a(n) = 2*n + a(n1) + 5, with n>0, a(0)=4.  Vincenzo Librandi, Aug 05 2010
a(n) = a(n).  Michael Somos, May 26 2014


MAPLE

A028875:=n>n^25; seq(A028875(n), n=0..100); # Wesley Ivan Hurt, Nov 13 2013


MATHEMATICA

Range[0, 49]^2  5 (* Alonso del Arte, Aug 27 2013 *)


PROG

(Sage) [lucas_number2(2, n, 2n) for n in xrange(1, 49)] # Zerinvary Lajos, Mar 12 2009
(MAGMA) [n^25: n in [0..50]]; // Wesley Ivan Hurt, May 22 2014


CROSSREFS

Cf. A028877 (subset of primes).
Sequence in context: A087707 A198352 A113011 * A130815 A084129 A011503
Adjacent sequences: A028872 A028873 A028874 * A028876 A028877 A028878


KEYWORD

sign,easy


AUTHOR

Patrick De Geest, Dec 11 1999


STATUS

approved



