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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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9
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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
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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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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
P. De Geest, Palindromic Sums of Squares of Consecutive Integers
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Index entries for two-way infinite sequences
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FORMULA
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a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2.
From Colin Barker, Mar 29 2012: (Start)
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
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MAPLE
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A027578:=n->5*(n+2)^2+10: seq(A027578(n), n=0..50); # Wesley Ivan Hurt, Nov 12 2015
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MATHEMATICA
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Table[5 (n + 2)^2 + 10, {n, 0, 50}] (* Bruno Berselli, Jul 29 2015 *)
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 xrange(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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Cf. A120328, A027575, A027865, A027580.
Subsequence of A174069-A174071.
Sequence in context: A304047 A174071 A006315 * A189712 A029713 A154599
Adjacent sequences: A027575 A027576 A027577 * A027579 A027580 A027581
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KEYWORD
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nonn,easy
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AUTHOR
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Patrick De Geest
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STATUS
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approved
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