0,2

n(n-3) (n >= 3) is the number of [body] diagonals of an n-gonal prism - Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr).

a(n) = A028387(n)-1. Half of the difference between n(n+1)(n+2)(n+3) and the largest square less than it. Calling this difference "SquareMod": a(n) = (1/2)*SqareMod(n(n+1)(n+2)(n+3)). - Rainer Rosenthal (r.rosenthal(AT)web.de), Sep 04 2004

n != -2 such that x^4 + x^3 - n*x^2 + x + 1 is reducible over the integers. Starting at 10: n such that x^4 + x^3 - n*x^2 + x + 1 is a product of irreducible quadratic factors over the integers. - James Buddenhagen (jbuddenh(AT)gmail.com), Apr 19 2005

If a 3-set Y and a 3-set Z, having two element in common, are subsets of an n-set X then a(n-4) is the number of 3-subests of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Oct 03 2007

Starting with offset 1 = binomial transform of [4, 6, 2, 0, 0, 0,...] [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 09 2009]

a(A002522(n)) = A156798(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 16 2009]

Except for the first term, a(n)=2*n+a(n-1)+2 (with a(1)=4) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 07 2009]

Milan Janjic, Two Enumerative Functions

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

a(n)=2*n+a(n-1) (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 29 2009]

For n=2, a(2)=2*2+0=4; n=3, a(3)=2*3+4=10; n=4, a(4)=2*4+10=18 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 29 2009]

a:=n->sum(binomial(n, 1), j=4..n): seq(a(n), n=3..47); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 12 2007

a:=n->sum(sum(3, j=3..n)/3, k=0..n): seq(a(n), n=2..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 30 2007

with (combinat):seq(fibonacci(3, n)+n-3, n=1..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2008

a:=n->sum(1+sum(1, k=5..n), k=1..n):seq(a(n), n=4...47); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 11 2008

with(finance):seq(add(cashflows([k, k, 2], 0 ), k=1..n), n=0..45); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]

lst={}; Do[AppendTo[lst, n*(n+3)], {n, 0, 6!, 1}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 07 2008]

Cf. A028387, A062145.

Cf. A002522.

Sequence in context: A009876 A161958 A013921 this_sequence A009877 A009880 A025712

Adjacent sequences: A028549 A028550 A028551 this_sequence A028553 A028554 A028555

nonn,easy,nice,new

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