This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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. Sequence in context: A156718 A007621 A051971 * A075004 A043222 A039399 Adjacent sequences:  A180271 A180272 A180273 * A180275 A180276 A180277 KEYWORD nonn,easy AUTHOR Zhining Yang, Jan 17 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 20 08:50 EDT 2018. Contains 313914 sequences. (Running on oeis4.)