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A110331
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Row sums of a number triangle related to the Pell numbers.
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8
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1, -1, -5, -11, -19, -29, -41, -55, -71, -89, -109, -131, -155, -181, -209, -239, -271, -305, -341, -379, -419, -461, -505, -551, -599, -649, -701, -755, -811, -869, -929, -991, -1055, -1121, -1189, -1259, -1331, -1405, -1481, -1559, -1639, -1721, -1805, -1891, -1979, -2069, -2161, -2255, -2351, -2449
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OFFSET
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0,3
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COMMENTS
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Row sums of A110330. Results from a general construction: the row sums of the inverse of the number triangle whose columns have e.g.f. (x^k/k!)/(1-a*x-b*x^2) have g.f. (1-(a+2)x-(2b-a-1)x^2)/(1-x)^3 and general term 1+(b-a)*n-b*n^2. This is the binomial transform of (1,-a,-2b,0,0,0,...).
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LINKS
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FORMULA
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a(n) = 1-n-n^2.
G.f.: (1-4*x+x^2)/(1-x)^3.
a(n) = binomial(n+2, 2) - 4*binomial(n+1, 2) + binomial(n, 2).
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MATHEMATICA
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CoefficientList[Series[(1-4x+x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 08 2012 *)
LinearRecurrence[{3, -3, 1}, {1, -1, -5}, 60] (* Harvey P. Dale, Mar 22 2022 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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