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A192928
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The Gi1 and Gi2 sums of Losanitsch's triangle A034851
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6
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1, 1, 1, 1, 2, 2, 3, 3, 5, 6, 9, 11, 16, 20, 29, 37, 53, 69, 98, 130, 183, 245, 343, 463, 646, 877, 1220, 1664, 2310, 3161, 4381, 6009, 8319, 11430, 15811, 21751, 30070, 41405, 57216, 78836, 108906, 150130, 207346
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OFFSET
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0,5
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COMMENTS
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The Gi1 and Gi2 sums, see A180662 for their definitions, of Losanitsch's triangle A034851 equal this sequence.
The a(n) are also the Ca1 and Ca2 sums of McGarvey’s triangle A102541.
Furthermore they are the Kn11 and Kn12 sums of triangle A228570.
And finally the terms of this sequence are the row sums of triangle A228572. (End)
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,0,-1,0,1,-1,0,0,-1).
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FORMULA
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G.f.: (-1/2)*(1/(x^4+x-1) + (1+x+x^4)/(x^8+x^2-1))= -(1+x)*(x^7-x^6+x^5+x-1) / ( (x^4+x-1)*(x^8+x^2-1) ).
a(n) = (A003269(n+1)+x(n)+x(n-1)+x(n-4))/2 with x(2*n) = A003269(n+1) and x(2*n+1) = 0.
a(n) = sum(A228570(n-k, k), k=0..floor(n/2))
a(n) = sum(A102541(n-2*k, k), k=0..floor(n/3))
a(n) = sum(A034851(n-3*k, k), k=0..floor(n/4)) (End)
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MAPLE
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A192928 := proc(n): (A003269(n+1)+x(n)+x(n-1)+x(n-4))/2 end: A003269 := proc(n): sum(binomial(n-1-3*j, j), j=0..(n-1)/3) end: x:=proc(n): if type(n, even) then A003269(n/2+1) else 0 fi: end: seq(A192928(n), n=0..42);
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MATHEMATICA
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LinearRecurrence[{1, 1, -1, 1, 0, -1, 0, 1, -1, 0, 0, -1}, {1, 1, 1, 1, 2, 2, 3, 3, 5, 6, 9, 11}, 43] (* Jean-François Alcover, Nov 16 2017 *)
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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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STATUS
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approved
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