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Search: id:A110331
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| A110331 |
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Row sums of a number triangle related to the Pell numbers. |
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+0
3
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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
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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,...).
Hankel transform of A007054(n)-2*0^n. - Paul Barry (pbarry(AT)wit.ie), Jul 20 2008
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FORMULA
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G.f.: (1-4x+x^2)/(1-x)^3; a(n)=binomial(n+2, 2)-4*binomial(n+1, 2)+binomial(n, 2); a(n)=1-n-n^2.
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MATHEMATICA
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f[n_]:=(n+(n+1))-(n+3)*n; lst={}; Do[AppendTo[lst, f[n]], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 08 2009]
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CROSSREFS
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Cf. A028387 (for absolute values).
Sequence in context: A088059 A165900 A028387 this_sequence A106071 A073847 A024833
Adjacent sequences: A110328 A110329 A110330 this_sequence A110332 A110333 A110334
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jul 20 2005
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