|
Search: id:A069778
|
|
|
| A069778 |
|
q-factorial numbers 3!_q. |
|
+0
5
|
|
| 1, 6, 21, 52, 105, 186, 301, 456, 657, 910, 1221, 1596, 2041, 2562, 3165, 3856, 4641, 5526, 6517, 7620, 8841, 10186, 11661, 13272, 15025, 16926, 18981, 21196, 23577, 26130, 28861, 31776, 34881, 38182, 41685, 45396, 49321
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
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]
|
|
REFERENCES
|
T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439-445.
|
|
LINKS
|
C. P. Simoes, Teste de Desempenho Mental.
|
|
FORMULA
|
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
|
|
EXAMPLE
|
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.
|
|
PROGRAM
|
(PARI) a(n)=(n+1)*(n^2+n+1)
|
|
CROSSREFS
|
Cf. A069777.
Adjacent sequences: A069775 A069776 A069777 this_sequence A069779 A069780 A069781
A001614 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]
Sequence in context: A028345 A097124 A135454 this_sequence A015644 A067680 A115052
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 07 2002
|
|
|
Search completed in 0.002 seconds
|
