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A243578
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Integers n of the form 8k+7 that are sum of distinct squares of the form m, m+1, m+2, m+4, where m == 1 (mod 4).
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6
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39, 191, 471, 879, 1415, 2079, 2871, 3791, 4839, 6015, 7319, 8751, 10311, 11999, 13815, 15759, 17831, 20031, 22359, 24815, 27399, 30111, 32951, 35919, 39015, 42239, 45591, 49071, 52679, 56415, 60279, 64271, 68391, 72639, 77015, 81519, 86151, 90911, 95799
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OFFSET
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1,1
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COMMENTS
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If n is of the form 8k+7 such that n=a^2+b^2+c^2+d^2 with gap pattern 112, then [a,b,c,d]=[1,2,3,5]+[4*i,4*i,4*i,4*i], i>=0.
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LINKS
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FORMULA
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a(n) = 64*n^2-40*n+15.
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>3.
G.f.: -x*(3*x+13)*(5*x+3) / (x-1)^3.
(End)
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EXAMPLE
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a(5)=64*5^2-40*5+15=1415 and m=4*5-3=17, and 1415=17^2+18^2+19^2+21^2.
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MAPLE
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A243578 := proc(n::posint) return 64*n^3-40*n+15 end;
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {39, 191, 471}, 50] (* Vincenzo Librandi, Sep 13 2015 *)
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PROG
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(PARI) Vec(-x*(3*x+13)*(5*x+3)/(x-1)^3 + O(x^100)) \\ Colin Barker, Sep 12 2015
(Magma) I:=[39, 191, 471]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..60]]; // Vincenzo Librandi, Sep 13 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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