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A145069
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a(n) = n*(n^2 + 3*n + 5)/3.
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1
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0, 3, 10, 23, 44, 75, 118, 175, 248, 339, 450, 583, 740, 923, 1134, 1375, 1648, 1955, 2298, 2679, 3100, 3563, 4070, 4623, 5224, 5875, 6578, 7335, 8148, 9019, 9950, 10943, 12000, 13123, 14314, 15575, 16908, 18315, 19798, 21359, 23000, 24723, 26530
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OFFSET
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0,2
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COMMENTS
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Old name was: Partial sums of A002061, starting at n=2.
Number of floating point dot operations (multiplications and divisions) in the factorization of an (n+1) X (n+1) real matrix by Gaussian elimination as, e.g., implemented in LINPACK subroutines sgefa.f or dgefa.f. The number of multiplications alone is given by A007290. The number of additions is given by A000330. - Hugo Pfoertner, Mar 28 2018
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LINKS
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FORMULA
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G.f.: x*(3-2*x+x^2)/(1-x)^4.
a(n) = a(n-1) + n^2 + n + 1 for n > 0, with a(0) = 0.
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EXAMPLE
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a(2) = a(1) + 2^2 + 2 + 1 = 3 + 4 + 2 + 1 = 10.
a(3) = a(2) + 3^2 + 3 + 1 = 10 + 9 + 3 + 1 = 23.
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MAPLE
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MATHEMATICA
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lst={}; s=0; Do[s+=n^2+n+1; AppendTo[lst, s-1], {n, 0, 5!}]; lst
CoefficientList[Series[x(3-2*x+x^2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 30 2012 *)
Table[n (n^2+3n+5)/3, {n, 0, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 3, 10, 23}, 50] (* Harvey P. Dale, Sep 10 2016 *)
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PROG
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(PARI) {a=0; for(n=1, 42, print1(a, ", "); a=a+n^2+n+1)} \\ adapted by Michel Marcus, Aug 23 2014
(Magma) I:=[0, 3, 10, 23]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 30 2012
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CROSSREFS
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Cf. A077415 (zero followed by partial sums of A028387, starting at n=1).
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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