A193578 a(n) = (13^n + 1)/2.
1, 7, 85, 1099, 14281, 185647, 2413405, 31374259, 407865361, 5302249687, 68929245925, 896080197019, 11649042561241, 151437553296127, 1968688192849645, 25592946507045379, 332708304591589921, 4325207959690668967, 56227703475978696565, 730960145187723055339, 9502481887440399719401
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..900
- Index entries for linear recurrences with constant coefficients, signature (14,-13).
Crossrefs
Cf. A141012.
Programs
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Magma
[(13^n+1)/2: n in [0..20]];
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Mathematica
(13^Range[0, 20] + 1)/2 (* Paolo Xausa, Mar 28 2025 *)
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PARI
a(n)=(13^n+1)/2 \\ Charles R Greathouse IV, Dec 27 2011
Formula
a(n) = 13*a(n-1) - 6, a(0)=1.
From Elmo R. Oliveira, Mar 25 2025: (Start)
G.f.: (1-7*x)/((1-x)*(1-13*x)).
E.g.f.: exp(7*x)*cosh(6*x).
a(n) = 14*a(n-1) - 13*a(n-2).
a(n) = A141012(n+1)/2. (End)