A089068 a(n) = a(n-1)+a(n-2)+a(n-3)+2 with a(0)=0, a(1)=0 and a(2)=1.

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

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

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (2,0,0,-1).

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

From Johannes W. Meijer, Sep 22 2010: (Start)

a(n) = a(n-1)+A001590(n+1).

a(n) = Sum_{m=0..n} A040000(m)*A000073(n-m).

a(n+2) = Sum_{k=0..floor(n/2)} A008288(n-k+1,k+1).

G.f. = x^2*(1+x)/((1-x)*(1-x-x^2-x^3)). (End)

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. A000931, A000073, A077939, A113300, A001057, A006054, A033505.

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

Adjacent sequences: A089065 A089066 A089067 * A089069 A089070 A089071

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