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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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10
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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]
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LINKS
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FORMULA
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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]
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MATHEMATICA
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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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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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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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