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 A089068 a(n) = a(n-1)+a(n-2)+a(n-3)+2 with a(0)=0, a(1)=0 and a(2)=1. 8
 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] Pairwise sums of A008937, A018921. [Johannes W. Meijer, Sep 21 2010] LINKS Index entries for linear recurrences with constant coefficients, signature (2,0,0,-1). [From Bruno Berselli, Sep 23 2010] FORMULA a(n) = A000073(n+2)-1. [From R. J. Mathar, Sep 22 2010] a(n) = a(n-1)+A001590(n+1) with a(0)=0. [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. [From 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: A162506 A227681 A055244 * A018180 A079735 A050243 Adjacent sequences:  A089065 A089066 A089067 * A089069 A089070 A089071 KEYWORD nonn 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

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