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A176177
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a(n) = 2*n*3^(n-1) - (3^n-1)/2.
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2
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0, 1, 8, 41, 176, 689, 2552, 9113, 31712, 108257, 364136, 1210505, 3985808, 13020305, 42249560, 136314617, 437641664, 1399018433, 4455335624, 14140847849, 44747066480, 141214768241, 444565011128, 1396457152601, 4377657815456, 13697832519329, 42788074776872, 133447955987273, 415595062931792, 1292538773705297, 4014877075845656
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: -x*(1+x) / ( (x-1)*(-1+3*x)^2 ). - R. J. Mathar, Sep 04 2013
The companion matrix of the polynomial x^3 - 7*x^2 + 15*x - 9 is [(1,0,0); (1,3,0); (1,4,3)] = M, then M^n * [1,1,1] generates the sequence, extracting the lower term. - Gary W. Adamson, Aug 10 2015
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MATHEMATICA
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Table[2n 3^(n-1)-(3^n-1)/2, {n, 0, 40}] (* or *) LinearRecurrence[{7, -15, 9}, {0, 1, 8}, 40] (* Harvey P. Dale, Jun 16 2014 *)
CoefficientList[Series[-x (1 + x)/((x - 1) (-1 + 3 x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 17 2014 *)
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PROG
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(Magma) I:=[0, 1, 8]; [n le 3 select I[n] else 7*Self(n-1)-15*Self(n-2)+9*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jun 17 2014
(PARI) first(m)=vector(m, n, 2*n*3^(n-1)-(3^n-1)/2); /* Anders Hellström, Aug 10 2015 */
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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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