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A180274 Integers whose squares are the sums of 24 consecutive squares. 2
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 (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

Table of n, a(n) for n=1..30.

K. S. Brown, Sum of Consecutive Nth Powers Equals an Nth Power

FORMULA

Conjecture: 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)), ", "))) }

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

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Last modified December 21 11:25 EST 2014. Contains 252310 sequences.