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A243578
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).
6
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
OFFSET
1,1
COMMENTS
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.
FORMULA
a(n) = 64*n^2-40*n+15.
From Colin Barker, Sep 12 2015: (Start)
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)
EXAMPLE
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.
MAPLE
A243578 := proc(n::posint) return 64*n^3-40*n+15 end;
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {39, 191, 471}, 50] (* Vincenzo Librandi, Sep 13 2015 *)
PROG
(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
KEYWORD
nonn,easy
AUTHOR
Walter Kehowski, Jun 08 2014
STATUS
approved