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A027575 a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2. 11
14, 30, 54, 86, 126, 174, 230, 294, 366, 446, 534, 630, 734, 846, 966, 1094, 1230, 1374, 1526, 1686, 1854, 2030, 2214, 2406, 2606, 2814, 3030, 3254, 3486, 3726, 3974, 4230, 4494, 4766, 5046, 5334, 5630, 5934, 6246, 6566, 6894, 7230, 7574 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Summation of n^2 taken 4 at a time. - Al Hakanson (hawkuu(AT)gmail.com), May 20 2009

LINKS

Table of n, a(n) for n=0..42.

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) = 4*n^2 + 12*n + 14. - Al Hakanson (hawkuu(AT)gmail.com), May 20 2009

a(n) = a(n-1)+8*(n+1) for n>0, a(0)=14. - Vincenzo Librandi, Nov 19 2010

G.f.: 2*(7-6*x+3*x^2)/(1-x)^3. - Colin Barker, Feb 17 2012

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

a(n) = (2*n+3)^2 + 5 = A016754(n+1) + 5, hence a(n) is never square.

a(n) is defined for n < 0 and a(-n) = a(n-3) for any n.

(End)

MATHEMATICA

f[n_]:=(n^2+(n+2)^2+(n+4)^2+(n+6)^2)/4; Table[f[n], {n, 0, 6!, 2}] (* Vladimir Joseph Stephan Orlovsky, Mar 03 2010 *)

Table[n^2 + (n + 1)^2 + (n + 2)^2 + (n + 3)^2, {n, 0, 42}] (* Alonso del Arte, Feb 17 2012 *)

Table[Total[Range[n, n+3]^2], {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {14, 30, 54}, 50] (* Harvey P. Dale, Jan 23 2017 *)

PROG

(Sage) [i^2+(i+1)^2+(i+2)^2+(i+3)^2 for i in xrange(0, 50)] # Zerinvary Lajos, Jul 03 2008

(PARI) vector(100, n, n--; n^2+(n+1)^2+(n+2)^2+(n+3)^2) \\ Altug Alkan, Nov 11 2015

CROSSREFS

Cf. A016754, A001844, A120328, A027578, A027865, A027577.

Sequence in context: A132759 A011257 A083540 * A104776 A101960 A075208

Adjacent sequences:  A027572 A027573 A027574 * A027576 A027577 A027578

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified October 22 14:41 EDT 2018. Contains 316486 sequences. (Running on oeis4.)