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A108765
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G.f. (1 - x + x^2)/((1-3*x)*(x-1)^2).
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4
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1, 4, 14, 45, 139, 422, 1272, 3823, 11477, 34440, 103330, 310001, 930015, 2790058, 8370188, 25110579, 75331753, 225995276, 677985846, 2033957557, 6101872691, 18305618094, 54916854304, 164750562935, 494251688829, 1482755066512
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OFFSET
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0,2
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COMMENTS
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Superseeker suggests a(n+2) - 2*a(n+1) + a(n) = 7*3^n = A005032(n).
Inverse binomial transform gives match with first differences of A026622.
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LINKS
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FORMULA
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a(0) = 1; a(n) = 3*a(n-1) + n.
a(n) = (7*3^n - 2*n - 3)/4. (End)
a(0)=1, a(1)=4, a(2)=14, a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3). - Harvey P. Dale, Dec 11 2012
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MATHEMATICA
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CoefficientList[Series[(1-x+x^2)/((1-3x)(x-1)^2), {x, 0, 40}], x] (* or *) LinearRecurrence[{5, -7, 3}, {1, 4, 14}, 40] (* Harvey P. Dale, Dec 11 2012 *)
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PROG
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Floretion Algebra Multiplication Program, FAMP Code: kbasefor[(- 'j + 'k - 'ii' - 'ij' - 'ik')], vesfor = A000004, Fortype: 1A, Roktype (leftfactor) is set to:Y[sqa.Findk()] = Y[sqa.Findk()] + Math.signum(Y[sqa.Findk()])*p (internal program code)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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