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A028875 n^2 - 5. 9
-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 (list; graph; refs; listen; history; text; internal format)
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: (n-3,n-2), ((n-1)*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, Near-Square Prime

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

FORMULA

G.f.: x^3*(-4+x+x^2)/(-1+x)^3. a(n) = 3a(n-1) - 3a(n-2) + a(n-3). - R. J. Mathar, Apr 28 2008

a(n) = 2*n + a(n-1) + 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^2-5; 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, 2-n) for n in xrange(-1, 49)] # Zerinvary Lajos, Mar 12 2009

(MAGMA) [n^2-5: n in [0..50]]; // Wesley Ivan Hurt, May 22 2014

(PARI) a(n)=n^2-5 \\ Charles R Greathouse IV, Oct 07 2015

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

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Last modified December 7 20:56 EST 2016. Contains 278895 sequences.