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A254283
Indices of hexagonal numbers (A000384) which are also centered triangular numbers (A005448).
3
1, 31, 115, 5965, 22261, 1157131, 4318471, 224477401, 837761065, 43547458615, 162521328091, 8447982493861, 31528299888541, 1638865056350371, 6116327657048815, 317931372949478065, 1186536037167581521, 61677047487142394191, 230181874882853766211
OFFSET
1,2
COMMENTS
Also positive integers x in the solutions to 4*x^2 - 3*y^2 - 2*x + 3*y - 2 = 0, the corresponding values of y being A254284.
FORMULA
a(n) = a(n-1)+194*a(n-2)-194*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+30*x^3-110*x^2+30*x+1) / ((x-1)*(x^2-14*x+1)*(x^2+14*x+1)).
EXAMPLE
31 is in the sequence because the 31st hexagonal number is 1891, which is also the 36th centered triangular number.
PROG
(PARI) Vec(-x*(x^4+30*x^3-110*x^2+30*x+1)/((x-1)*(x^2-14*x+1)*(x^2+14*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 28 2015
STATUS
approved