login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A189374 Expansion of 1/((1-x)^5*(x^2+x+1)^3). 4
1, 2, 3, 7, 11, 15, 25, 35, 45, 65, 85, 105, 140, 175, 210, 266, 322, 378, 462, 546, 630, 750, 870, 990, 1155, 1320, 1485, 1705, 1925, 2145, 2431, 2717, 3003, 3367, 3731, 4095, 4550, 5005, 5460, 6020, 6580, 7140, 7820 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The Ca1(n) and Ze3(n) triangle sums of A139600 lead to the sequence given above, see the formulas. For the definitions of these triangle sums see A180662.
LINKS
FORMULA
a(n) = (2*a(n-1) + 2*a(n-2) + (8+n)*a(n-3))/n with a(0)=1, a(1)=2, a(2)=3 and a(3)=7.
a(n) = sum(A011779(n-k)*A049347(k), k=0..n).
Ca1(n) = A189374(n-3) - A189374(n-4) - A189374(n-6) + 2*A189374(n-7).
Ze3(n) = 2*A189374(n-3) - A189374(n-4) - 2*A189374(n-6) + 5*A189374(n-7) with A189374(n)=0 for n <= -1.
a(n) = (floor(n/3)+1)*(floor(n/3)+2)*(floor(n/3)+3)*(3*floor(n/3)+4*(4-(3*floor((n+3)/3)-n)))/24. - Luce ETIENNE, Jun 29 2015
MAPLE
a:= proc(n) option remember; `if` (n<4, [1, 2, 3, 7][n+1], (2*a(n-1) +2*a(n-2) +(8+n) *a(n-3))/n) end: seq (a(n), n=0..50);
CROSSREFS
Sequence in context: A174060 A285278 A092353 * A180516 A100963 A342029
KEYWORD
easy,nonn
AUTHOR
Johannes W. Meijer, Apr 29 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)