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A131253
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Row sums of triangle A131252.
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3
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1, 3, 8, 17, 34, 64, 117, 209, 368, 641, 1108, 1904, 3257, 5551, 9432, 15985, 27030, 45616, 76845, 129245, 217056, 364033, 609768, 1020192, 1705009, 2846619, 4748072, 7912529, 13174858, 21919456, 36440613, 60538409, 100503632, 166744961, 276476092, 458151440
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (k+1)*(Sum_{i=0..k} binomial(n-k, k-i)).
a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 4*a(n-4) - a(n-6).
G.f.: (1 - x - x^3)/((1 - x)^2*(1 - x - x^2)^2).
(End)
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EXAMPLE
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a(3) = 17 = sum of row 3 terms of A131252: (7 + 6 + 3 + 1).
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MATHEMATICA
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LinearRecurrence[{4, -4, -2, 4, 0, -1}, {1, 3, 8, 17, 34, 64}, 40] (* Vincenzo Librandi, Aug 10 2018 *)
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PROG
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(PARI) Vec((1 - x - x^3)/((1 - x)^2*(1 - x - x^2)^2) + O(x^40)) \\ Andrew Howroyd, Aug 09 2018
(PARI) a(n)={sum(k=0, n, (k+1)*sum(i=0, k, binomial(n-k, k-i)))} \\ Andrew Howroyd, Aug 09 2018
(Magma) I:=[1, 3, 8, 17, 34, 64]; [n le 6 select I[n] else 4*Self(n-1)- 4*Self(n-2)-2*Self(n-3)+4*Self(n-4)-Self(n-6): n in [1..40]]; // Vincenzo Librandi, Aug 10 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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