# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a294364 Showing 1-1 of 1 %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 Index entries for linear recurrences with constant coefficients, 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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE