A275766 a(n) = (5^(2*(n + 1)) - 1)/4.

156, 3906, 97656, 2441406, 61035156, 1525878906, 38146972656, 953674316406, 23841857910156, 596046447753906, 14901161193847656, 372529029846191406, 9313225746154785156, 232830643653869628906, 5820766091346740722656, 145519152283668518066406

Offset: 1

Author

Gionata Neri, Aug 07 2016

Keywords

• nonn
• easy

Comments

It seems that these terms are the only numbers n such that n and n + 1 are in A053696.

Examples

			3906 written in base 5 is 111111 and 3907 written in base 62 is 111.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..700
• Index entries for linear recurrences with constant coefficients, signature (26,-25).

Crossrefs

Cf. A003463, A053696, A125831.

Programs

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 *)

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

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