|
|
A263943
|
|
Positive integers n such that (n+21)^3 - n^3 is a square.
|
|
8
|
|
|
7, 119, 4564, 32900, 1161895, 8359127, 295119412, 2123188004, 74959171399, 539281396535, 19039334418580, 136975351534532, 4835915983150567, 34791200008377239, 1228303620385828084, 8836827826776286820, 311984283662017185415, 2244519476801168477687
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
a(n) = a(n-1)+254*a(n-2)-254*a(n-3)-a(n-4)+a(n-5) for n>5.
G.f.: 7*x*(4*x^4+16*x^3-381*x^2-16*x-1) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)).
|
|
EXAMPLE
|
7 is in the sequence because (7+21)^3 - 7^3 = 147^2.
|
|
MATHEMATICA
|
LinearRecurrence[{1, 254, -254, -1, 1}, {7, 119, 4564, 32900, 1161895}, 20] (* Harvey P. Dale, Jan 11 2017 *)
|
|
PROG
|
(PARI) Vec(7*x*(4*x^4+16*x^3-381*x^2-16*x-1)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)) + O(x^30))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|