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A027578
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Sums of five consecutive squares: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2.
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10
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30, 55, 90, 135, 190, 255, 330, 415, 510, 615, 730, 855, 990, 1135, 1290, 1455, 1630, 1815, 2010, 2215, 2430, 2655, 2890, 3135, 3390, 3655, 3930, 4215, 4510, 4815, 5130, 5455, 5790, 6135, 6490, 6855, 7230, 7615, 8010, 8415, 8830, 9255, 9690, 10135, 10590, 11055
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OFFSET
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0,1
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COMMENTS
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a(n) is defined for n < 0 and a(-n) = a(n-4) for any n; a(-3) = a(-1) = 15, a(-2) = 10. - Jean-Christophe Hervé, Nov 11 2015
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LINKS
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FORMULA
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G.f.: 5*(6-7*x+3*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. (End)
a(n) = 5*(n + 2)^2 + 10. a(n) is never square. - Bruno Berselli, Jul 29 2015
Sum_{n>=0} 1/a(n) = coth(sqrt(2)*Pi)*Pi/(10*sqrt(2)) - 7/60.
Sum_{n>=0} (-1)^n/a(n) = cosech(sqrt(2)*Pi)*Pi/(10*sqrt(2)) + 1/60. (End)
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MAPLE
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MATHEMATICA
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Total/@Partition[Range[0, 50]^2, 5, 1] (* or *) LinearRecurrence[{3, -3, 1}, {30, 55, 90}, 50] (* Harvey P. Dale, Mar 06 2018 *)
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PROG
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(Sage) [i^2+(i+1)^2+(i+2)^2+(i+3)^2+(i+4)^2 for i in range(0, 50)] # Zerinvary Lajos, Jul 03 2008
(Magma) [n^2+(n+1)^2+(n+2)^2+(n+3)^2+(n+4)^2: n in [0..50] ]; // Vincenzo Librandi, Jun 17 2011
(PARI) vector(100, n, n--; n^2+(n+1)^2+(n+2)^2+(n+3)^2+(n+4)^2) \\ Altug Alkan, Nov 11 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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