A241955 a(n) = 2^(4*n+3) - 1.
7, 127, 2047, 32767, 524287, 8388607, 134217727, 2147483647, 34359738367, 549755813887, 8796093022207, 140737488355327, 2251799813685247, 36028797018963967, 576460752303423487, 9223372036854775807, 147573952589676412927, 2361183241434822606847, 37778931862957161709567
Offset: 0
Links
- Jens Kruse Andersen, Table of n, a(n) for n = 0..100
- Index entries for linear recurrences with constant coefficients, signature (17,-16).
Programs
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Magma
[2^(4*n+3)-1 : n in [0..20]]; // Wesley Ivan Hurt, Aug 15 2014
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Maple
A241955:=n->2^(4*n+3)-1: seq(A241955(n), n=0..20); # Wesley Ivan Hurt, Aug 15 2014
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Mathematica
Table[2^(4n + 3) - 1, {n, 0, 29}] 2^(4 Range[0, 20] + 3) - 1 (* Wesley Ivan Hurt, Aug 15 2014 *) -
PARI
vector(40, n, 2^(4*n-1)-1) \\ Derek Orr, Aug 11 2014
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PARI
Vec((8*x+7)/((x-1)*(16*x-1)) + O(x^100)) \\ Colin Barker, Aug 11 2014
Formula
From Colin Barker, Aug 11 2014: (Start)
a(n) = 17*a(n-1) - 16*a(n-2).
G.f.: (8*x+7)/((x-1)*(16*x-1)). (End)
E.g.f.: exp(x)*(8*exp(15*x) - 1). - Elmo R. Oliveira, Feb 20 2025