

A094196


Indices of the start of a string of 24 consecutive squares whose sum is a square.


10



1, 9, 20, 25, 44, 76, 121, 197, 304, 353, 540, 856, 1301, 2053, 3112, 3597, 5448, 8576, 12981, 20425, 30908, 35709, 54032, 84996, 128601, 202289, 306060, 353585, 534964, 841476, 1273121, 2002557, 3029784, 3500233, 5295700, 8329856, 12602701
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The sequence could also include 11, 8 and 4; and if N is in the sequence, then so is 23N.
Equivalently, 24*a(n)^2 + 552*a(n) + 4324 is a square.
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(np)  x(n2p) + 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


LINKS

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,10,10,0,0,0,0,1,1).


FORMULA

Recurrence: a(n+12) = 10a(n+6)  a(n) + 92.
O.g.f.: x*(18*x11*x^25*x^319*x^432*x^535*x^6+4*x^7+3*x^8+x^9+3*x^10+4*x^11+4*x^12) / ((1+x) * (110*x^6+x^12)).  R. J. Mathar, Dec 02 2007
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(n1)+10*a(n6)10*a(n7)a(n12)+a(n13).  Harvey P. Dale, Oct 10 2011
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(n6)a(n12) + 92 for n>12.  Daniel Mondot, Aug 05 2016


MATHEMATICA

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 *)


PROG

(PARI) for(n=1, 15000000, if(issquare(sum(j=n, n+23, j^2)), print1(n, ", "))) \\ Klaus Brockhaus, Jun 01 2004


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



