|
|
A274603
|
|
Numbers n such that 2*n+1 and 3*n+1 are both triangular numbers.
|
|
5
|
|
|
45, 4455, 436590, 42781410, 4192141635, 410787098865, 40252943547180, 3944377680524820, 386508759747885225, 37873914077612227275, 3711257070846250387770, 363665319028854925774230, 35635490007756936475486815, 3491914355441150919671933685
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
a(n+1) / a(n) goes to 49 + 20*sqrt(6) when n goes to infinity.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 99*a(n-1)-99*a(n-2)+a(n-3) for n>3.
G.f.: 45*x / ((1-x)*(1-98*x+x^2)).
(End)
|
|
EXAMPLE
|
45 is a term because 2*45 + 1 = 91 and 3*45 + 1 = 136 are both triangular numbers.
|
|
PROG
|
(PARI) isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(3*n+1, 3);
(PARI) Vec(45*x/((1-x)*(1-98*x+x^2)) + O(x^20)) \\ Colin Barker, Jun 30 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|