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!)
A089068 a(n) = a(n-1)+a(n-2)+a(n-3)+2 with a(0)=0, a(1)=0 and a(2)=1. 10
0, 0, 1, 3, 6, 12, 23, 43, 80, 148, 273, 503, 926, 1704, 3135, 5767, 10608, 19512, 35889, 66011, 121414, 223316, 410743, 755475, 1389536, 2555756, 4700769, 8646063, 15902590, 29249424, 53798079, 98950095, 181997600, 334745776, 615693473 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
The a(n+2) represent the Kn12 and Kn22 sums of the square array of Delannoy numbers A008288. See A180662 for the definition of these knight and other chess sums. [Johannes W. Meijer, Sep 21 2010]
LINKS
FORMULA
a(n) = A008937(n-2)+A008937(n-1). - Johannes W. Meijer, Sep 21 2010
a(n) = A018921(n-5)+A018921(n-4), n>4. - Johannes W. Meijer, Sep 21 2010
a(n) = A000073(n+2)-1. [R. J. Mathar, Sep 22 2010]
a(n) = a(n-1)+A001590(n+1). [Johannes W. Meijer, Sep 22 2010]
a(n) = sum(A040000(m)*A000073(n-m),m=0..n). [Johannes W. Meijer, Sep 22 2010]
a(n+2) = add(A008288(n-k+1,k+1),k=0..floor(n/2)). [Johannes W. Meijer, Sep 22 2010]
G.f. = x^2*(1+x)/((1-x)*(1-x-x^2-x^3)). [Johannes W. Meijer, Sep 22 2010]
a(n) = 2*a(n-1)-a(n-4), a(0)=0, a(1)=0, a(2)=1, a(3)=3. [Bruno Berselli, Sep 23 2010]
MATHEMATICA
Join[{a=0, b=0, c=1}, Table[d=a+b+c+2; a=b; b=c; c=d, {n, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *)
RecurrenceTable[{a[0]==a[1]==0, a[2]==1, a[n]==a[n-1]+a[n-2]+a[n-3]+2}, a[n], {n, 40}] (* or *) LinearRecurrence[{2, 0, 0, -1}, {0, 0, 1, 3}, 40] (* Harvey P. Dale, Sep 19 2011 *)
CROSSREFS
Cf. A000073 (Kn11 & Kn21), A089068 (Kn12 & Kn22), A180668 (Kn13 & Kn23), A180669 (Kn14 & Kn24), A180670 (Kn15 & Kn25). [Johannes W. Meijer, Sep 21 2010]]
Sequence in context: A328609 A227681 A055244 * A018180 A079735 A341580
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Dec 03 2003
EXTENSIONS
Corrected and information added by Johannes W. Meijer, Sep 22 2010, Oct 22, 2010
Definition based on arbitrarily set floating-point precision removed - R. J. Mathar, Sep 30 2010
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 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)