1,3

3*a(n)+1 is a perfect square.

Could also be called generalized octagonal numbers, or n(3n-2) for n=0, +- 1, +- 2,.... Cf. A001318, generalized pentagonal numbers. - Matthew Vandermast (ghodges14(AT)comcast.net), Apr 10 2003

n^2 - n - floor(n/2)^2.

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

Number of units of a(n) belongs to a periodic sequence: 0, 1, 5, 8, 6, 1, 3, 0, 6, 5, 5, 6, 0, 3, 1, 6, 8, 5, 1, 0. [From Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 04 2009]

Index entries for sequences related to linear recurrences with constant coefficients

R. Stephan, On the solutions to 'px+1 is square'

G.f.: sum_{n=0..inf} (-1)^n*[x^(a(2n+1)) + x^(a(2n+2))] = 1/1 - (x-x^2)/1 - (x^2-x^4)/1 - (x^3-x^6)/1 -...- (x^k - x^(2k))/1 -... (continued fraction where k=1..inf). - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 16 2002

a(2n)=n(3n+2), a(2n+1)=3*n^2+4n+1. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007

a(n+1) = ceil(n/2)^2+A046092([n/2]).

a(2n)=n(3n-2)=A000567(n), a(2n+1)=n(3n+2)=A045944(n). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007

O.g.f.: -x^2*(x^2+4*x+1)/((x-1)^3*(1+x)^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 15 2008

a(n+1)-a(n)=A022998(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 15 2008

(PARI) a(n)=if(n%2, (n-1)*(3*n+1)/4, n*(3*n-4)/4)

Partial sums of A022998.

Cf. A005563, A046092.

Sequence in context: A141536 A065905 A126695 this_sequence A030006 A088586 A073136

Adjacent sequences: A001079 A001080 A001081 this_sequence A001083 A001084 A001085

nonn,easy

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

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 19 2000

More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 25 2003

Some of the formulae were corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 15 2008