OFFSET
0,1
COMMENTS
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
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Patrick De Geest, Palindromic Sums of Squares of Consecutive Integers.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 5*A059100(n+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
E.g.f.: 5*(6 + 5*x + x^2)*exp(x). - G. C. Greubel, Aug 24 2022
From Amiram Eldar, Sep 15 2022: (Start)
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)
MAPLE
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved