|
|
A096942
|
|
Fifth column of (1,5)-Pascal triangle A096940.
|
|
3
|
|
|
5, 21, 55, 115, 210, 350, 546, 810, 1155, 1595, 2145, 2821, 3640, 4620, 5780, 7140, 8721, 10545, 12635, 15015, 17710, 20746, 24150, 27950, 32175, 36855, 42021, 47705, 53940, 60760, 68200, 76296, 85085, 94605, 104895, 115995, 127946, 140790, 154570
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
If Y is a 5-subset of an n-set X then, for n>=8, a(n-8) is the number of 4-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 08 2007
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (n+20)*binomial(n+3, 3)/4 = 5*b(n) - 4*b(n-1), with b(n) = A000332(n+4) = binomial(n+4, 4).
G.f.: (5-4*x)/(1-x)^5.
|
|
MATHEMATICA
|
Table[(n + 20) Binomial[n + 3, 3]/4, {n, 0, 100}]
CoefficientList[Series[(5 - 4 x)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 01 2013 *)
|
|
PROG
|
(Magma) [(n + 20)*Binomial(n + 3, 3) div 4: n in [0..50]]; // Vincenzo Librandi, Oct 01 2013
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|