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A027865 Sums of six consecutive squares: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 + (n+5)^2. 8
55, 91, 139, 199, 271, 355, 451, 559, 679, 811, 955, 1111, 1279, 1459, 1651, 1855, 2071, 2299, 2539, 2791, 3055, 3331, 3619, 3919, 4231, 4555, 4891, 5239, 5599, 5971, 6355, 6751, 7159, 7579, 8011 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From Jean-Christophe Hervé, Nov 11 2015: (Start)

a(n) is defined for n < 0 and a(-n) = a(n-5) for any n; a(-4) = a(-1) = 31, a(-3) = a(-2) = 19.

a(n) == 3 (mod 4) for all n in Z, hence a(n) is never square.

(End)

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

P. De Geest, World!Of Numbers

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Index entries for two-way infinite sequences

FORMULA

a(n) = 6*n^2 + 30*n + 55.

G.f.: ( -55+74*x-31*x^2 ) / (x-1)^3. - R. J. Mathar, Jun 11 2013

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 12*(n+2). - Jean-Christophe Hervé, Nov 11 2015

MAPLE

A027865:=n->6*n^2 + 30*n + 55: seq(A027865(n), n=0..60); # Wesley Ivan Hurt, Nov 12 2015

MATHEMATICA

Table[Total@ Map[#^2 &, n + Range[0, 5]], {n, 0, 34}] (* Michael De Vlieger, Nov 12 2015 *)

PROG

(Sage) [i^2+(i+1)^2+(i+2)^2+(i+3)^2+(i+4)^2+(i+5)^2 for i in xrange(0, 36)] # Zerinvary Lajos, Jul 03 2008

(MAGMA) [n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 + (n+5)^2: n in [0..50] ]; // Vincenzo Librandi, Jun 17 2011

(PARI) a(n)=6*n^2+30*n+55 \\ Charles R Greathouse IV, Jul 28 2015

(PARI) Vec((-31*x^2+74*x-55)/(x-1)^3 + O(x^50)) \\ Altug Alkan, Nov 12 2015

CROSSREFS

Cf. A027575, A027578, A120328.

Sequence in context: A039533 A157484 A230125 * A247681 A195118 A143205

Adjacent sequences:  A027862 A027863 A027864 * A027866 A027867 A027868

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest

EXTENSIONS

Corrected by Ralf Stephan, Jan 02 2005

Edited by Charles R Greathouse IV, Jul 25 2010

Renamed by Jean-Christophe Hervé, Nov 12 2015

STATUS

approved

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Last modified February 19 20:48 EST 2018. Contains 299357 sequences. (Running on oeis4.)