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A243581
Integers of the form 8k + 7 that can be written as a sum of four distinct squares of the form m, m + 2, m + 3, m + 4, where m == 2 (mod 4).
6
119, 351, 711, 1199, 1815, 2559, 3431, 4431, 5559, 6815, 8199, 9711, 11351, 13119, 15015, 17039, 19191, 21471, 23879, 26415, 29079, 31871, 34791, 37839, 41015, 44319, 47751, 51311, 54999, 58815, 62759, 66831, 71031, 75359, 79815
OFFSET
1,1
COMMENTS
If n is of the form 8k + 7 and n = a^2 + b^2 + c^2 + d^2 where [a, b, c, d] has gap pattern 122, then [a, b, c, d] = [3, 5, 6, 7] + [4*i, 4*i, 4*i, 4*i], i >= 0.
FORMULA
a(n) = 64*n^2 + 40*n + 15.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Colin Barker, Jun 09 2014
G.f.: -x*(15*x^2-6*x+119) / (x-1)^3. - Colin Barker, Jun 09 2014
EXAMPLE
a(5) = 64*5^2 + 40*5 + 15 = 1815 and 4*5 - 1 = 19 so 1815 = 19^2 + 21^2 + 22^2 + 23^2.
MAPLE
A243581 := proc(n::posint) return 64*n^2+40*n+15 end;
MATHEMATICA
Table[64n^2 + 40n + 15, {n, 50}] (* Alonso del Arte, Jun 08 2014 *)
LinearRecurrence[{3, -3, 1}, {119, 351, 711}, 50] (* Harvey P. Dale, Jul 23 2014 *)
PROG
(PARI) Vec(-x*(15*x^2-6*x+119)/(x-1)^3 + O(x^100)) \\ Colin Barker, Jun 09 2014
(Magma) [ 64*n^2 + 40*n + 15 : n in [1..50] ]; // Wesley Ivan Hurt, Jun 11 2014
KEYWORD
nonn,easy
AUTHOR
Walter Kehowski, Jun 08 2014
STATUS
approved