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%I #34 Oct 19 2017 10:38:27
%S 1,9,20,25,44,76,121,197,304,353,540,856,1301,2053,3112,3597,5448,
%T 8576,12981,20425,30908,35709,54032,84996,128601,202289,306060,353585,
%U 534964,841476,1273121,2002557,3029784,3500233,5295700,8329856,12602701
%N Indices of the start of a string of 24 consecutive squares whose sum is a square.
%C The sequence could also include -11, -8 and -4; and if N is in the sequence, then so is -23-N.
%C Equivalently, 24*a(n)^2 + 552*a(n) + 4324 is a square.
%C All sequences of this type (i.e., sequences with fixed offset k, and a discernible pattern: k=0...23 for this sequence, k=0...22 for A269447, k=0..1 for A001652) can be extended using a formula such as x(n) = a*x(n-p) - x(n-2p) + b, where a and b are various constants, and p is the period of the series. Alternatively, 'p' can be considered the number of concurrent series. - _Daniel Mondot_, Aug 05 2016
%H Daniel Mondot, <a href="/A094196/b094196.txt">Table of n, a(n) for n = 1..106</a>
%H K. S. Brown, <a href="http://www.mathpages.com/home/kmath147.htm">Sum of Consecutive Nth Powers Equals an Nth Power</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,10,-10,0,0,0,0,-1,1).
%F Recurrence: a(n+12) = 10a(n+6) - a(n) + 92.
%F O.g.f.: x*(-1-8*x-11*x^2-5*x^3-19*x^4-32*x^5-35*x^6+4*x^7+3*x^8+x^9+3*x^10+4*x^11+4*x^12) / ((-1+x) * (1-10*x^6+x^12)). - _R. J. Mathar_, Dec 02 2007
%F a(0)=1, a(1)=9, a(2)=20, a(3)=25, a(4)=44, a(5)=76, a(6)=121, a(7)=197, a(8)=304, a(9)=353, a(10)=540, a(11)=856, a(12)=1301; thereafter a(n) = a(n-1)+10*a(n-6)-10*a(n-7)-a(n-12)+a(n-13). - _Harvey P. Dale_, Oct 10 2011
%F a(1)=1, a(2)=9, a(3)=20, a(4)=25, a(5)=44, a(6)=76, a(7)=121, a(8)=197, a(9)=304, a(10)=353, a(11)=540, a(12)=856; a(n)=10*a(n-6)-a(n-12) + 92 for n>12. - _Daniel Mondot_, Aug 05 2016
%t LinearRecurrence[{1,0,0,0,0,10,-10,0,0,0,0,-1,1},{1,9,20,25,44,76,121,197,304,353,540,856,1301},60] (* _Harvey P. Dale_, Oct 10 2011 *)
%o (PARI) for(n=1,15000000,if(issquare(sum(j=n,n+23,j^2)),print1(n,","))) \\ _Klaus Brockhaus_, Jun 01 2004
%Y Cf. A001032, A001652, A106521, A269447.
%K nonn,easy
%O 1,2
%A _Lekraj Beedassy_, May 25 2004
%E More terms from _Don Reble_ (djr(AT)hotmail.com) and _Klaus Brockhaus_, Jun 01 2004
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