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 A180274 Integers whose squares are the sums of 24 consecutive squares. 13
 70, 106, 158, 182, 274, 430, 650, 1022, 1546, 1786, 2702, 4250, 6430, 10114, 15302, 17678, 26746, 42070, 63650, 100118, 151474, 174994, 264758, 416450, 630070, 991066, 1499438, 1732262, 2620834, 4122430, 6237050, 9810542, 14842906, 17147626, 25943582 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The corresponding starts of 24 consecutive squares to be summed are A094196. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 K. S. Brown, Sum of Consecutive Nth Powers Equals an Nth Power V. Pletser, Finding all squared integers expressible as the sum of consecutive squared integers using generalized Pell equation solutions with Chebyshev polynomials, arXiv preprint arXiv:1409.7972 [math.NT], 2014. See Table 2 p. 8. Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,10,0,0,0,0,0,-1). FORMULA a(n) = +10*a(n-6) -a(n-12). G.f. ( 70+106*x+158*x^2+182*x^3+274*x^4+430*x^5-50*x^6-38*x^7-34*x^8-34*x^9-38*x^10-50*x^11 ) / ( 1-10*x^6+x^12 ). - Joerg Arndt, Jan 17 2011 a(n) = sqrt( 24*(A094196(n))^2 +552*A094196(n)+4324) . - R. J. Mathar, Jan 20 2011 MAPLE A094196 := proc(n) if n <= 12 then op(n, [1, 9, 20, 25, 44, 76, 121, 197, 304, 353, 540, 856]) ; else 10*procname(n-6)-procname(n-12)+92 ; end if ; end proc: A180274 := proc(n) local a96 ; a96 := A094196(n) ; 24*a96^2+552*a96+4324 ; sqrt(%) ; end proc: seq(A180274(n), n=1..30) ; # R. J. Mathar, Jan 20 2011 MATHEMATICA Select[Sqrt[#]&/@(Total[#]&/@Partition[Range[900000]^2, 24, 1]), IntegerQ] (* Harvey P. Dale, Jan 21 2011 *) t={70, 106, 158, 182, 274, 430, 650, 1022, 1546, 1786, 2702, 4250}; Do[AppendTo[t, 10*t[[-6]] - t[[-12]]], {n, 13, 100}]; t PROG (PARI) { for(n=1, 999999, t=((n+23)*(n+24)*(2*n+47)-n*(n-1)*(2*n-1))/6; if(issquare(t), print1(ceil(sqrt(t)), ", "))) } (PARI) Vec(-2*x*(25*x^11+19*x^10+17*x^9+17*x^8+19*x^7+25*x^6-215*x^5-137*x^4-91*x^3-79*x^2-53*x-35) / (x^12-10*x^6+1) + O(x^100)) \\ Colin Barker, May 09 2015 CROSSREFS Cf. A094196. Cf. A001032 (24 is a term of that sequence). Sequence in context: A007621 A353061 A051971 * A075004 A043222 A039399 Adjacent sequences: A180271 A180272 A180273 * A180275 A180276 A180277 KEYWORD nonn,easy AUTHOR Zhining Yang, Jan 17 2011 STATUS approved

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Last modified August 8 12:42 EDT 2024. Contains 375021 sequences. (Running on oeis4.)