cp's OEIS Frontend

A294364 Linear recurrence with signature (1,1,-1,1,1), where the first terms are powers of 2 (1,2,4,8,16).

%I A294364 #9 Oct 29 2017 13:31:39
%S A294364 1,2,4,8,16,23,37,56,94,152,250,401,649,1046,1696,2744,4444,7187,
%T A294364 11629,18812,30442,49256,79702,128957,208657,337610,546268,883880,
%U A294364 1430152,2314031,3744181,6058208,9802390,15860600,25662994,41523593,67186585,108710174,175896760,284606936
%N A294364 Linear recurrence with signature (1,1,-1,1,1), where the first terms are powers of 2 (1,2,4,8,16).
%C A294364 The interest of this sequence mainly lies in the peculiarities of its array of successive differences, which begins:
%C A294364 1,    2,   4,   8,  16,  23,  37,  56,  94, ...
%C A294364 1,    2,   4,   8,   7,  14,  19,  38,  58, ...
%C A294364 1,    2,   4,  -1,   7,   5,  19,  20,  40, ...
%C A294364 1,    2,  -5,   8,  -2,  14,   1,  20,  13, ...
%C A294364 1,   -7,  13, -10,  16, -13,  19,  -7,  31, ...
%C A294364 -8,  20, -23,  26, -29,  32, -26,  38, -23, ...
%C A294364 28, -43,  49, -55,  61, -58,  64, -61,  67, ...
%C A294364 The main diagonal is A000079 (powers of 2).
%C A294364 The first upper subdiagonal is A254076.
%C A294364 The second upper subdiagonal (4, 8, 7, 14, 19, 38, ...) is not in the OEIS.
%C A294364 The third upper subdiagonal is A185346 (2^n-9).
%C A294364 Every row, once computed mod 9, is 6-periodic, repeating (1, 2, 4, 8, 7, 5) (A153130).
%H A294364 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,1,1).
%F A294364 G.f.: (1+x+x^2+3*x^3+5*x^4) / (1-x-x^2+x^3-x^4-x^5).
%F A294364 a(n) = (9/2)*fibonacci(n) + (-1)^n - sqrt(3)*sin(n*Pi/3).
%F A294364 a(n) ~ (9/2)*fibonacci(n).
%t A294364 LinearRecurrence[{1, 1, -1, 1, 1}, {1, 2, 4, 8, 16}, 40]
%Y A294364 Cf. A000045, A000079, A153130, A185346, A254076.
%K A294364 nonn,easy
%O A294364 0,2
%A A294364 _Jean-François Alcover_ and _Paul Curtz_, Oct 29 2017