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A080855
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(9*n^2-3*n+2)/2.
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6
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1, 4, 16, 37, 67, 106, 154, 211, 277, 352, 436, 529, 631, 742, 862, 991, 1129, 1276, 1432, 1597, 1771, 1954, 2146, 2347, 2557, 2776, 3004, 3241, 3487, 3742, 4006, 4279, 4561, 4852, 5152, 5461, 5779, 6106, 6442, 6787, 7141, 7504, 7876, 8257, 8647, 9046
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OFFSET
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0,2
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COMMENTS
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The old definition of this sequence was "Generalized polygonal numbers".
Row T(3,n) of A080853.
Equals binomial transform of [1, 3, 9, 0, 0, 0,...] - Gary W. Adamson, Apr 30 2008
a(n) is also the least weight of self-conjugate partitions having n different parts such that each part is congruent to 2 modulo 3. The first such self-conjugate partitions, corresponding to a(n)=1,2,3,4, are 2+2, 5+5+2+2+2, 8+8+5+5+5+2+2+2, 11+11+8+8+8+5+5+5+2+2+2. [Augustine O. Munagi (amunagi(AT)yahoo.com), Dec 18 2008]
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=3, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=3, a(n-1)=-coeff(charpoly(A,x),x^(n-2)). [Milan Janjic, Jan 27 2010]
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REFERENCES
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A. O. Munagi, Pairing conjugate partitions by residue classes, Discrete Math., 308 (2008), 2492--2501.
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LINKS
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Table of n, a(n) for n=0..45.
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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G.f.: (1+x+7*x^2)/(1-x)^3.
a(n) = 9*n+a(n-1)-6 with n>0, a(0)=1. [Vincenzo Librandi, Aug 08 2010]
a(n) = n*A005448(n+1)-(n-1)*A005448(n), with A005448(0)=1. [Bruno Berselli, Jan 15 2013]
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MATHEMATICA
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s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 500, 9}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
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CROSSREFS
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Cf. A027468, A038764. [From Augustine O. Munagi (amunagi(AT)yahoo.com), Dec 18 2008]
Sequence in context: A054246 A173545 A080709 * A203299 A198015 A103770
Adjacent sequences: A080852 A080853 A080854 * A080856 A080857 A080858
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Feb 23 2003
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EXTENSIONS
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Definition replaced with the closed form by Bruno Berselli, Jan 15 2013
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STATUS
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approved
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