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A275766
a(n) = (5^(2*(n + 1)) - 1)/4.
1
156, 3906, 97656, 2441406, 61035156, 1525878906, 38146972656, 953674316406, 23841857910156, 596046447753906, 14901161193847656, 372529029846191406, 9313225746154785156, 232830643653869628906, 5820766091346740722656, 145519152283668518066406
OFFSET
1,1
COMMENTS
It seems that these terms are the only numbers n such that n and n + 1 are in A053696.
FORMULA
a(n) = ((A125831(n+1))^3 - 1)/(A125831(n+1) - 1) - 1.
a(n) = A003463(2*(n+1)).
a(n) = 26*a(n-1) - 25*a(n-2), a(1) = 156, a(2) = 3906.
G.f.: 6*x*(26-25*x) / ((1-x)*(1-25*x)). - Colin Barker, Aug 24 2016
EXAMPLE
3906 written in base 5 is 111111 and 3907 written in base 62 is 111.
MATHEMATICA
Table[(5^(2 (n + 1)) - 1)/4, {n, 16}] (* or *)
Rest@ CoefficientList[Series[6 x (26 - 25 x)/((1 - x) (1 - 25 x)), {x, 0, 16}], x] (* Michael De Vlieger, Aug 28 2016 *)
PROG
(PARI) Vec(6*x*(26-25*x)/((1-x)*(1-25*x)) + O(x^20)) \\ Colin Barker, Aug 24 2016
(PARI) a(n) = 5^(2*n+2)\4 \\ Charles R Greathouse IV, Aug 28 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gionata Neri, Aug 07 2016
STATUS
approved