This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A180668 a(n) = a(n-1)+a(n-2)+a(n-3)+4*n-8 with a(0)=0, a(1)=0 and a(2)=1. 5
 0, 0, 1, 5, 14, 32, 67, 133, 256, 484, 905, 1681, 3110, 5740, 10579, 19481, 35856, 65976, 121377, 223277, 410702, 755432, 1389491, 2555709, 4700720, 8646012, 15902537, 29249369, 53798022, 98950036, 181997539, 334745713 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The a(n+2) represent the Kn13 and Kn23 sums of the square array of Delannoy numbers A008288. See A180662 for the definition of these knight and other chess sums. LINKS Index entries for linear recurrences with constant coefficients, signature (3,-2,0,-1,1). FORMULA a(n) = a(n-1)+a(n-2)+a(n-3)+4*n-8 with a(0)=0, a(1)=0 and a(2)=1. a(n) = a(n-1)+A001590(n+3)-2 with a(0)=0. a(n) = sum(A008574(m)*A000073(n-m),m=0..n). a(n+2) = add(A008288(n-k+2,k+2),k=0..floor(n/2)). GF(x) = (x^2*(1+x)^2)/((1-x)^2*(1-x-x^2-x^3)). Contribution from Bruno Berselli, Sep 23 2010: (Start) a(n) = 2*a(n-1)-a(n-4)+4 for n>4. a(n)-3*a(n-1)+2a(n-2)+a(n-4)-a(n-5) = 0 for n>4. (End) MAPLE nmax:=31: a(0):=0: a(1):=0: a(2):=1: for n from 3 to nmax do a(n):= a(n-1)+a(n-2)+a(n-3)+4*n-8 od: seq(a(n), n=0..nmax); CROSSREFS Cf. A000073 (Kn11 & Kn21), A089068 (Kn12 & Kn22), A180668 (Kn13 & Kn23), A180669 (Kn14 & Kn24), A180670 (Kn15 & Kn25). Sequence in context: A266759 A139754 A036595 * A053209 A271993 A274324 Adjacent sequences:  A180665 A180666 A180667 * A180669 A180670 A180671 KEYWORD easy,nonn AUTHOR Johannes W. Meijer, Sep 21 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 15 19:35 EST 2019. Contains 319171 sequences. (Running on oeis4.)