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A179297
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a(n) = n^2 - (n-1)^2 - (n-2)^2 - ... - 1^2.
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4
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1, 3, 4, 2, -5, -19, -42, -76, -123, -185, -264, -362, -481, -623, -790, -984, -1207, -1461, -1748, -2070, -2429, -2827, -3266, -3748, -4275, -4849, -5472, -6146, -6873, -7655, -8494, -9392, -10351, -11373, -12460, -13614, -14837, -16131
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x*(1+x)*(1-2*x)/(1-x)^4. a(n) = -n*(1-9*n+2*n^2)/6 = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). [From R. J. Mathar, Jul 11 2010]
a(0)=1, a(1)=3, a(2)=4, a(3)=2, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) From Harvey P. Dale, Jul 11 2012
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EXAMPLE
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1^2-0=1,
2^2-1=3,
3^2-2^2-1=4,
4^2-3^2-2^2-1=2,
5^2-4^2-3^2-2^2-1=-5,
...
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MATHEMATICA
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f[n_]:=Module[{k=n-1, x=n^2}, While[k>0, x-=k^2; k--; ]; x]; lst={}; Do[AppendTo[lst, f[n]], {n, 5!}]; lst
CoefficientList[Series[-(1+x)*(2*x-1)/(x-1)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 04 2012 *)
nn=40; Module[{lst=Range[nn]^2, sublst}, Table[sublst=Take[lst, n]; Last[ sublst]- Total[Most[sublst]], {n, nn}]] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {1, 3, 4, 2}, 40] (* Harvey P. Dale, Jul 11 2012 *)
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PROG
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(Magma) I:=[1, 3, 4, 2]; [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, Jul 04 2012
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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