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A253175
Indices of hexagonal numbers (A000384) which are also centered hexagonal numbers (A003215).
5
1, 7, 67, 661, 6541, 64747, 640927, 6344521, 62804281, 621698287, 6154178587, 60920087581, 603046697221, 5969546884627, 59092422149047, 584954674605841, 5790454323909361, 57319588564487767, 567405431320968307, 5616734724645195301, 55599941815130984701
OFFSET
1,2
COMMENTS
Also positive integers x in the solutions to 4*x^2-6*y^2-2*x+6*y-2 = 0, the corresponding values of y being A253475.
FORMULA
a(n) = 11*a(n-1)-11*a(n-2)+a(n-3).
G.f.: -x*(x^2-4*x+1) / ((x-1)*(x^2-10*x+1)).
a(n) = (2+(5-2*sqrt(6))^n*(3+sqrt(6))-(-3+sqrt(6))*(5+2*sqrt(6))^n)/8. - Colin Barker, Mar 05 2016
4*a(n) = 1+3*A072256(n). - R. J. Mathar, Feb 07 2022
EXAMPLE
7 is in the sequence because the 7th hexagonal number is 91, which is also the 6th centered hexagonal number.
PROG
(PARI) Vec(-x*(x^2-4*x+1)/((x-1)*(x^2-10*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 08 2015
STATUS
approved