A113870 - OEIS

%I #15 Jul 08 2024 21:33:54

%S 1,3,7,39,103,615,1639,9831,26215,157287,419431,2516583,6710887,

%T 40265319,107374183,644245095,1717986919,10307921511,27487790695,

%U 164926744167,439804651111,2638827906663,7036874417767,42221246506599

%N a(n) = a(n-1) + 2^(k(n)), where k(n) is the n-th term of the sequence formed by k(1)=0 together with the numbers A042963.

%H Vincenzo Librandi, <a href="/A113870/b113870.txt">Table of n, a(n) for n = 1..300</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 16, -16).

%F G.f.: (3+x-40*x^2)/(4*(-1+x)*(-1+4*x)*(1+4*x)). - _Vaclav Kotesovec_, Nov 28 2012

%o (PARI) a(n)=([0,1,0; 0,0,1; -16,16,1]^(n-1)*[1;3;7])[1,1] \\ _Charles R Greathouse IV_, Jul 08 2024

%Y Cf. A099974, A112627, A080355, A080567, A099969, A099970, A099971.

%K nonn,easy

%O 1,2

%A _Artur Jasinski_, Jan 27 2006

%E Edited with better definition and offset corrected by _Omar E. Pol_, Jan 08 2009