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A262077
The first of thirteen consecutive positive integers the sum of the squares of which is equal to the sum of the squares of seven consecutive positive integers.
4
15, 435, 66543, 1388283, 209496225, 4370333325, 659494068633, 13757807937693, 2076087118579335, 43309575017543115, 6535521589793696823, 136338528397417807203, 20573819888583439038345, 429193644085496239550805, 64766378473739076299032113
OFFSET
1,1
COMMENTS
For the first of the corresponding seven consecutive positive integers, see A262076.
FORMULA
a(n) = a(n-1)+3148*a(n-2)-3148*a(n-3)-a(n-4)+a(n-5) for n>5.
G.f.: 3*x*(9*x^4+140*x^3-6296*x^2-140*x-5) / ((x-1)*(x^4-3148*x^2+1)).
EXAMPLE
15 is in the sequence because 15^2 + ... + 27^2 = 5915 = 26^2 + ... + 32^2.
MATHEMATICA
LinearRecurrence[{1, 3148, -3148, -1, 1}, {15, 435, 66543, 1388283, 209496225}, 20] (* Vincenzo Librandi, Sep 11 2015 *)
PROG
(PARI) Vec(3*x*(9*x^4+140*x^3-6296*x^2-140*x-5)/((x-1)*(x^4-3148*x^2+1)) + O(x^20))
(Magma) I:=[15, 435, 66543, 1388283, 209496225]; [n le 5 select I[n] else Self(n-1)+3148*Self(n-2)-3148*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Sep 11 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Sep 10 2015
STATUS
approved