|
|
A096957
|
|
Fourth column (m=3) of (1,6)-Pascal triangle A096956.
|
|
4
|
|
|
6, 19, 40, 70, 110, 161, 224, 300, 390, 495, 616, 754, 910, 1085, 1280, 1496, 1734, 1995, 2280, 2590, 2926, 3289, 3680, 4100, 4550, 5031, 5544, 6090, 6670, 7285, 7936, 8624, 9350, 10115, 10920, 11766, 12654, 13585, 14560, 15580, 16646, 17759, 18920
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
If Y is a 6-subset of an n-set X then, for n>=8, a(n-8) is the number of 3-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 16 2007
|
|
LINKS
|
|
|
FORMULA
|
a(n) = A096956(n+3, 3) = 6*b(n) - 5*b(n-1) = (n+18)*binomial(n+2, 2)/3, with b(n):=A000292(n)=binomial(n+3, 3).
G.f.: (6-5*x)/(1-x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - Vincenzo Librandi, Apr 19 2017
|
|
MATHEMATICA
|
CoefficientList[Series[(6 - 5*x)/(1 - x)^4, {x, 0, 40}], x] (* Wesley Ivan Hurt, Apr 18 2017 *)
LinearRecurrence[{4, -6, 4, -1}, {6, 19, 40, 70}, 50] (* Vincenzo Librandi, Apr 19 2017 *)
|
|
PROG
|
(Magma) I:=[6, 19, 40, 70]; [n le 4 select I[n] else 4*Self(n-1)- 6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Apr 19 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|