|
|
A033445
|
|
a(n) = (n - 1)*(n^2 + n - 1).
|
|
7
|
|
|
1, 0, 5, 22, 57, 116, 205, 330, 497, 712, 981, 1310, 1705, 2172, 2717, 3346, 4065, 4880, 5797, 6822, 7961, 9220, 10605, 12122, 13777, 15576, 17525, 19630, 21897, 24332, 26941, 29730, 32705, 35872, 39237, 42806, 46585, 50580, 54797, 59242, 63921
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Binomial transform of 1, -6, 6, 0, 0, 0, (0 continued). - R. J. Mathar, Nov 29 2015
|
|
REFERENCES
|
Graham et al., Handbook of Combinatorics, Vol. 2, p. 1243.
|
|
LINKS
|
|
|
FORMULA
|
a(0)=1, a(1)=0, a(2)=5; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 6. - Gionata Neri, May 12 2015
O.g.f.: (1 - 4*x + 11*x^2 - 2*x^3)/(1-x)^4.
E.g.f.: (1 - x + 3*x^2 + x^3)*exp(x). (End)
|
|
MAPLE
|
|
|
MATHEMATICA
|
LinearRecurrence[{4, -6, 4, -1}, {1, 0, 5, 22}, 50] (* Harvey P. Dale, Dec 28 2021 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|