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
Fun With Num3ers, Sets of 24 consecutive squares whose sum is a square, July 27 2016.
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
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:
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
KEYWORD
nonn,easy
AUTHOR
Zhining Yang, Jan 17 2011
STATUS
approved