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A294364
Linear recurrence with signature (1,1,-1,1,1), where the first terms are powers of 2 (1,2,4,8,16).
0
1, 2, 4, 8, 16, 23, 37, 56, 94, 152, 250, 401, 649, 1046, 1696, 2744, 4444, 7187, 11629, 18812, 30442, 49256, 79702, 128957, 208657, 337610, 546268, 883880, 1430152, 2314031, 3744181, 6058208, 9802390, 15860600, 25662994, 41523593, 67186585, 108710174, 175896760, 284606936
OFFSET
0,2
COMMENTS
The interest of this sequence mainly lies in the peculiarities of its array of successive differences, which begins:
1, 2, 4, 8, 16, 23, 37, 56, 94, ...
1, 2, 4, 8, 7, 14, 19, 38, 58, ...
1, 2, 4, -1, 7, 5, 19, 20, 40, ...
1, 2, -5, 8, -2, 14, 1, 20, 13, ...
1, -7, 13, -10, 16, -13, 19, -7, 31, ...
-8, 20, -23, 26, -29, 32, -26, 38, -23, ...
28, -43, 49, -55, 61, -58, 64, -61, 67, ...
The main diagonal is A000079 (powers of 2).
The first upper subdiagonal is A254076.
The second upper subdiagonal (4, 8, 7, 14, 19, 38, ...) is not in the OEIS.
The third upper subdiagonal is A185346 (2^n-9).
Every row, once computed mod 9, is 6-periodic, repeating (1, 2, 4, 8, 7, 5) (A153130).
FORMULA
G.f.: (1+x+x^2+3*x^3+5*x^4) / (1-x-x^2+x^3-x^4-x^5).
a(n) = (9/2)*fibonacci(n) + (-1)^n - sqrt(3)*sin(n*Pi/3).
a(n) ~ (9/2)*fibonacci(n).
MATHEMATICA
LinearRecurrence[{1, 1, -1, 1, 1}, {1, 2, 4, 8, 16}, 40]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved