1,1

These numbers cannot be perfect squares. See the link for a proof.

2nd elementary symmetric polynomial of n,n+1 and n+2: n(n+1)+n(n+2)+(n+1)(n+2). - Zak Seidov (zakseidov(AT)yahoo.com), Mar 23 2005

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)

This sequence equals for n=>2 the third right hand column of triangle A165674. Its recurrence relation leads to Pascal's triangle A007318. Crowley's formula for A080663[n-1] leads to Wiggen's triangle A028421 and the o.g.f. of this sequence, without the first term, leads to Wood's polynomials A126671. See also A165676, A165677, A165678 and A165679.

(End)

E. Grosswald, Topics from the Theory of Numbers, 1966 p 64 problem 11

Cino Hilliard, 3n^2-1 not square .

Eric Weisstein's World of Mathematics, Symmetric Polynomial

a(n) = unsigned real term in (1 + ni)^3. E.g. (1 + 4i)^3 = (-47 - 52i); where 52 = A121670(4). Note that (4 + i)^3 = (52 + 47i) = (A121670(4) + A080663(4)i). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 14 2006

A080663[n-1]=3*n^2+6*n+2 [From Stephen Crowley (crow(AT)crowlogic.net), Jul 06 2009]

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)

Recurrence relation a(n) = a(n-1) - 3* a(n-2) + 3*a(n-3)

O.g.f. for sequence without a(1): Gf(z) = (0*z^4 -2*z^3+7*z^2-11*z)/(z-1)^3

(End)

a(n)=6*n+a(n-1)-3 (with a(1)=2) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 11 2009]

For n=2, a(2)=6*2+2-3=11; n=3, a(3)=6*3+11-3=26; n=4, a(4)=6*4+26-3=47 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 11 2009]

(PARI) nosquare(n) = { for(x=1, n, y = 3*x*x-1; print1(y" ") ) } checkit(n) = { for(x=1, n, y = 3*x*x-1; if(!issquare(y), print1(y" ")) ) }

Cf. A121670.

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)

Equals for n=>2 the third right hand column of A165674.

(End)

Sequence in context: A077482 A141428 A104085 this_sequence A141464 A139211 A161527

Adjacent sequences: A080660 A080661 A080662 this_sequence A080664 A080665 A080666

easy,nonn,new

Cino Hilliard (hillcino368(AT)gmail.com), Mar 01 2003