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URL: https://oeis.org/A243579

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A243579
Integers of the form 8k+7 that can be written as a sum of four distinct squares of the form m, m+2, m+4, m+5, where m == 1 (mod 4).
6
71, 255, 567, 1007, 1575, 2271, 3095, 4047, 5127, 6335, 7671, 9135, 10727, 12447, 14295, 16271, 18375, 20607, 22967, 25455, 28071, 30815, 33687, 36687, 39815, 43071, 46455, 49967, 53607, 57375, 61271, 65295, 69447, 73727, 78135, 82671, 87335, 92127, 97047, 102095, 107271, 112575, 118007, 123567, 129255, 135071, 141015, 147087
OFFSET
1,1
COMMENTS
If n is of the form 8k+7 and n = a^2+b^2+c^2+d^2 with gap pattern 221, then [a,b,c,d] = [1,3,5,6]+[4*i,4*i,4*i,4*i] for i>=0.
FORMULA
a(n) = 64*n^2-8*n+15.
From Colin Barker, Sep 13 2015: (Start)
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>3.
G.f.: x*(15*x^2+42*x+71) / (1-x)^3. (End)
EXAMPLE
a(5) = 64*5^2-8*5+15 = 1575 and m = 4*5-3 = 17 so 1575 = 17^2+19^2+21^2+22^2.
MAPLE
A243579 := proc(n::posint) return 64*n^2-8*n+15 end;
PROG
(PARI) Vec(-x*(15*x^2+42*x+71)/(x-1)^3 + O(x^100)) \\ Colin Barker, Sep 13 2015
(Magma) [64*n^2-8*n+15 : n in [1..50]]; // Wesley Ivan Hurt, Nov 28 2021
KEYWORD
nonn,easy
AUTHOR
Walter Kehowski, Jun 08 2014
STATUS
approved