2,2

Sequence allows us to find X values of the equation: X^3 + 4*X^2 = Y^2. To find Y values: b(n)=n*(n^2 - 4). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007

Discriminants of binary forms x^2 + n*x*y + y^2 (for n>1) - Artur Jasinski (grafix(AT)csl.pl), Apr 28 2008

Number of units of a(n) belongs to a periodic sequence: 0, 5, 2, 1, 2, 5, 0, 7, 6, 7. [From Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 04 2009]

A. Connes, Noncommutative Geometry, Academic Press, 1994, p. 35.

Index entries for sequences related to linear recurrences with constant coefficients

Eric Weisstein's World of Mathematics, Near-Square Prime

Except for initial term, denominators of wavelengths of hydrogen lines.

a(n+2)=n(n+4). G.f.(x)=x^3*(5-3*x)/(1-x)^3 - Barry E. Williams, Jun 16 2000, R. J. Mathar, Aug 06 2009

Except for the first term, a(n)=2*n+a(n-1)+3 (with a(1)=5) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 07 2009]

a:=n->sum(n, j=5..n): seq(a(n), n=4..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 12 2007

with(combinat):seq(fibonacci(3, i)-5, i=2..43); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008

with(finance):seq(add(cashflows([k, k, 3], 0 ), k=1..n), n=0..45); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]

lst={}; Do[AppendTo[lst, n^2-4], {n, 2, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 06 2008]

(Other) SAGE: [lucas_number2(2, n, 2) for n in xrange(2, 44)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 12 2009]

a(n), n>=3, second column (used for the Balmer series of the hydrogen atom) of triangle A120070.

Cf. A005563, A046092, A001082, A002378, A036666, A062717.

Sequence in context: A063559 A121291 A097984 this_sequence A038794 A131976 A074376

Adjacent sequences: A028344 A028345 A028346 this_sequence A028348 A028349 A028350

nonn,new

N. J. A. Sloane (njas(AT)research.att.com).

Formula adapted to the offset by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 06 2009