The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A198862 Sum of the n-th antidiagonal in the triangle A192011. 1
-1, 2, 2, 2, 3, 1, -1, -3, -6, -7, -6, -3, 3, 10, 16, 19, 16, 6, -10, -29, -45, -51, -41, -12, 33, 84, 125, 137, 104, 20, -105, -242, -346, -366, -261, -19, 327, 693, 954, 973, 646, -47, -1001, -1974, -2620, -2573, -1572, 402, 3022 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The current sequence and its successive differences are:
-1, 2, 2, 2, 3, 1, -1 ,-3, -6, -7, ...
3, 0, 0, 1, -2, -2, -2, -3, -1, 1, 3, 6, 7, 6, 3, -3, -10, -16, ...
-3, 0, 1, -3, 0, 0, -1, 2, 2, 2, 3, 1, -1, -3, -6, -7, -6, ...
3, 1, -4, 3, 0, -1, 3, 0, 0, 1, -2, -2, -2, -3, -1, 1, 3, 6, 7, ...
-2, -5, 7, -3, -1, 4, -3, 0, 1, -3, 0, 0, -1, 2, 2, 2, 3, 1, ...
-3, 12, -10, 2, 5, -7, 3, 1, -4, 3, 0, -1, 3, 0, 0, 1, -2, ...
15, -22, 12, 3, -12, 10, -2, -5, 7, -3, -1, 4, -3, 0, ...
-37, 34, -9, -15, 22, -12, -3, 12, -10, 2, 5, -7, 3, 1, -4, ...
Each row obeys the same linear recurrence and is a version of the row 4 lines farther up in the same array shifted right by 12 places.
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/2)} A192011(n-k,k).
a(n) = a(n-1) - a(n-4), n > 3.
From R. J. Mathar, Nov 02 2011: (Start)
G.f.: (-1 + 3*x) / (1 - x + x^4).
a(n) = 3*A099530(n-1) - A099530(n). (End)
MAPLE
A198862 := proc(n)
add( A192011(n-k, k), k=0..floor(n/2)) ;
end proc:
seq(A198862(n), n=0..80) ; # R. J. Mathar, Nov 03 2011
CROSSREFS
Sequence in context: A162203 A071455 A288724 * A349227 A264025 A139465
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Oct 30 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 May 17 19:53 EDT 2024. Contains 372607 sequences. (Running on oeis4.)