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A027578 Sums of five consecutive squares: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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

FORMULA

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

MAPLE

A027578:=n->5*(n+2)^2+10: seq(A027578(n), n=0..50); # Wesley Ivan Hurt, Nov 12 2015

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 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

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified December 15 13:23 EST 2018. Contains 318149 sequences. (Running on oeis4.)