2,2

Number of edges in the join of two star graphs, each of order n, S_n * S_n - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002

Sequence allows us to find X values of the equation: X^3 + (X - 3)^2 + X - 6 = Y^2. To prove that X = n^2 + 4n + 1: Y^2 = X^3 + (X - 3)^2 + X - 6 = X^3 + X^2 - 5X + 3 = (X + 3)(X^2 - 2X + 1) = (X + 3)*(X - 1)^2 it means: X = 1 or (X + 3) must be a perfect square, so X = k^2 - 3 with k>=2. we can put: k = n + 2, which gives: X = n^2 + 4n + 1 and Y = (n + 2)(n^2 + 4n). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 29 2007

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 29 2009: (Start)

Let C = 2 + sqrt(3) = 3.732...; and 1/C = .267...; then a(n) =

(n - 2 + C) * (n - 2 + 1/C). Example: a(5) = 46 = (5 + 3.732...)*(5 + .267...). (End)

Except for the first term, a(n)=2*n+a(n-1)+3 (with a(1)=6) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 07 2009]

P. De Geest, Palindromic Quasipronics of the form n(n+x)

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

O.g.f.: x^2*(-1-3*x+2*x^2)/(-1+x)^3. a(n) = 3a(n-1)-3a(n-2)+a(n-3). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2008

Equals binomial transform of [1, 5, 2, 0, 0, 0,...] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 30 2008

a(n)=2*n+a(n-1)+1 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 29 2009]

a(n)= floor((n^4+2*n^3)/(n^2+1)) [From Gary Detlefs (gdetlefs(AT)aol.com), Feb 20 2010]

For n=2, a(2)=2*2+1+1=6; n=3, a(3)=2*3+6+1=13; n=4, a(4)=2*4+13+1=22 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 29 2009]

with(combinat, fibonacci):seq(fibonacci(3, i)-4, i=2..48); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008

seq(floor(n^4+2*n^3)/(n^2+1)), n=1..47); [From Gary Detlefs (gdetlefs(AT)aol.com), Feb 20 2010]

lst={}; Do[AppendTo[lst, n^2-3], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 27 2009]

s = 1; lst = {s}; Do[s += n; AppendTo[lst, s], {n, 5, 100, 2}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]

sage: [lucas_number1(3, n, 3) for n in xrange(2, 50)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 03 2008

Cf. A117950, A132411, A132414, A002522.

Sequence in context: A056115 A101247 A072212 this_sequence A049718 A036707 A054311

Adjacent sequences: A028869 A028870 A028871 this_sequence A028873 A028874 A028875

nonn,new

Patrick De Geest (pdg(AT)worldofnumbers.com)