0,2

Number of proper n-colorings of the 4-cycle with one vertex color fixed (offset 2). - Michael Somos, Jul 19 2002

n such that x^3 + x^2 + x + n factors over the integers. - James Buddenhagen (jbuddenh(AT)gmail.com), Apr 19 2005

If Y is a 4-subset of an n-set X then, for n>=5, a(n-5) is the number of 5-subsets of X having at least two elements in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 08 2007

Equals row sums of the Connell (A001614) sequence as a triangle:/Q 1;/Q 2, 4;/Q 5, 7, 9;/Q 10, 12, 14, 16;/Q ... [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]

T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439-445.

C. P. Simoes, Teste de Desempenho Mental.

a(n) = (n + 1)(n^2 + n + 1)

a(n)=(n+1)^3-2*T(n) where T(n) is the n-th triangular number: n*(n+1)/2 (A000217) 1^3-2x0=1; 2^3-2x1=6; 3^3-2x3=21; 4^3-2x6=52; 5^3-2*10=105 - Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 14 2006

For 2-colorings only 1212 is proper so a(2-2)=1. The proper 3-colorings are: 1212,1313,1213,1312,1232,1323 so a(3-2)=6.

n->sum(-2+sum(2-sum(2, j=1..n), j=1..n), j=1..n):seq(a(n)/(-2), n=1..40); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 06 2008]

a[n_]:=n^3-n^2+n^1; lst={}; Do[AppendTo[lst, a[n]], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 22 2008]

(PARI) a(n)=(n+1)*(n^2+n+1)

Cf. A069777.

A001614 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]

Sequence in context: A028345 A097124 A135454 this_sequence A015644 A067680 A115052

Adjacent sequences: A069775 A069776 A069777 this_sequence A069779 A069780 A069781

easy,nonn

Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 07 2002