A199110 a(n) = 7*3^n + 1.
8, 22, 64, 190, 568, 1702, 5104, 15310, 45928, 137782, 413344, 1240030, 3720088, 11160262, 33480784, 100442350, 301327048, 903981142, 2711943424, 8135830270, 24407490808, 73222472422, 219667417264, 659002251790, 1977006755368, 5931020266102, 17793060798304, 53379182394910
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-3).
Programs
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Magma
[7*3^n+1: n in [0..30]];
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Mathematica
7*3^Range[0, 30] + 1 (* Paolo Xausa, Jan 28 2025 *)
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Python
def a(n): return 7*3**n + 1 print([a(n) for n in range(26)]) # Michael S. Branicky, Aug 22 2021
Formula
a(n) = 3*a(n-1) - 2 = A005032(n) + 1.
a(n) = 4*a(n-1) - 3*a(n-2).
From Bruno Berselli, Nov 03 2011: (Start)
G.f.: 2*(4-5*x)/((1-x)*(1-3*x)).
a(n) = 2*A199109(n). (End)
E.g.f.: exp(x)*(1 + 7*exp(2*x)). - Elmo R. Oliveira, Apr 02 2025