login
A252985
Numbers n such that the sum of the hexagonal numbers X(n) and X(n+1) is equal to the heptagonal number H(m) for some m.
2
1, 579, 1870, 835278, 2696899, 1204470657, 3888926848, 1736845852476, 5607829818277, 2504530514800095, 8086486709028946, 3611531265495884874, 11660708226589922215, 5207825580314551188573, 16814733176255958805444, 7509680875282317318037752
OFFSET
1,2
COMMENTS
Also positive integers x in the solutions to 8*x^2-5*y^2+4*x+3*y+2 = 0, the corresponding values of y being A252986.
FORMULA
a(n) = a(n-1)+1442*a(n-2)-1442*a(n-3)-a(n-4)+a(n-5).
G.f.: x*(68*x^3+151*x^2-578*x-1) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)).
EXAMPLE
1 is in the sequence because X(1)+X(2) = 1+6 = 7 = H(2).
PROG
(PARI) Vec(x*(68*x^3+151*x^2-578*x-1)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Dec 25 2014
STATUS
approved