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 A027575 a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2. 13
 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 Terms are congruent to (2,0,0) mod 6. - Ezhilarasu Velayutham, Apr 04 2019 LINKS 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) = 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 HervĂ©, Nov 11 2015: (Start) a(n) = (2*n+3)^2 + 5 = A016754(n+1) + 5, hence a(n) is never square. The last formula defines a(n) for n < 0; then we have a(-n) = a(n-3) for all n. (End) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Wesley Ivan Hurt, Apr 16 2021 MATHEMATICA 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 *) Total/@Partition[Range[0, 50]^2, 4, 1] (* Harvey P. Dale, Feb 08 2020 *) PROG (Sage) [i^2+(i+1)^2+(i+2)^2+(i+3)^2 for i in range(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 A308312 A101960 Adjacent sequences:  A027572 A027573 A027574 * A027576 A027577 A027578 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified August 1 22:01 EDT 2021. Contains 346408 sequences. (Running on oeis4.)