[go: up one dir, main page]

login
A253714
Indices of hexagonal numbers (A000384) which are also centered heptagonal numbers (A069099).
3
1, 2857, 45529, 184300369, 2937241777, 11889953986681, 189493215939721, 767068491312421537, 12224965330197902689, 49486656636639609035209, 788681413122894278122297, 3192582165489099245985035761, 50880992673985436128583949841
OFFSET
1,2
COMMENTS
Also positive integers x in the solutions to 4*x^2-7*y^2-2*x+7*y-2 = 0, the corresponding values of y being A253715.
FORMULA
a(n) = a(n-1)+64514*a(n-2)-64514*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+2856*x^3-21842*x^2+2856*x+1) / ((x-1)*(x^2-254*x+1)*(x^2+254*x+1)).
EXAMPLE
2857 is in the sequence because the 2857th hexagonal number is 16322041, which is also the 2160th centered heptagonal number.
PROG
(PARI) Vec(-x*(x^4+2856*x^3-21842*x^2+2856*x+1)/((x-1)*(x^2-254*x+1)*(x^2+254*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 10 2015
STATUS
approved