|
|
A257940
|
|
y-values in the solutions to x^2 + x = 5*y^2 + y.
|
|
2
|
|
|
0, 1, 52, 357, 16776, 114985, 5401852, 37024845, 1739379600, 11921885137, 560074829380, 3838809989301, 180342355680792, 1236084894669817, 58069678454385676, 398015497273691805, 18698256119956506912, 128159754037234091425, 6020780400947540840020
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Also, numbers k such that 2*k^2 + k*(k+1)/2 is a triangular number. Example: 114985 is a term because 2*114985^2 + 114985*114986/2 = 257114*257115/2. - Bruno Berselli, Mar 02 2018
|
|
LINKS
|
|
|
FORMULA
|
a(1) = 0, a(2) = 1, a(3) = 52, a(4) = 357, a(5) = 16776; for n > 5, a(n) = a(n-1) + 322*a(n-2) - 322*a(n-3) - a(n-4) + a(n-5).
a(n) = 322*a(n-2) - a(n-4) + 32.
a(n) = 72*A257939(n-2) + 161*a(n-2) + 52.
G.f.: x^2*(3*x^3+17*x^2-51*x-1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)). - Colin Barker, May 14 2015
|
|
MATHEMATICA
|
LinearRecurrence[{1, 322, -322, -1, 1}, {0, 1, 52, 357, 16776}, 30] (* Vincenzo Librandi, May 15 2015 *)
|
|
PROG
|
(Magma) I:=[0, 1, 52, 357, 16776]; [n le 5 select I[n] else Self(n-1)+322*Self(n-2)-322*Self(n-3)-Self(n-4)+Self(n-5): n in [1..19]];
(PARI) concat(0, Vec((3*x^3+17*x^2-51*x-1)/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))) \\ Colin Barker, May 14 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|