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A089068
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a(n) = a(n-1)+a(n-2)+a(n-3)+2 with a(0)=0, a(1)=0 and a(2)=1.
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9
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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
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OFFSET
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0,4
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COMMENTS
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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]
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LINKS
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Table of n, a(n) for n=0..34.
Index entries for linear recurrences with constant coefficients, signature (2,0,0,-1). [From Bruno Berselli, Sep 23 2010]
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FORMULA
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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]
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MATHEMATICA
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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 *)
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CROSSREFS
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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 A050243
Adjacent sequences: A089065 A089066 A089067 * A089069 A089070 A089071
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula, Dec 03 2003
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EXTENSIONS
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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
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STATUS
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approved
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