A254076 -id:A254076 - 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).

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

Jean-François Alcover and Paul Curtz, Oct 29 2017

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).

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,1).

Cf. A000045, A000079, A153130, A185346, A254076.

LinearRecurrence[{1, 1, -1, 1, 1}, {1, 2, 4, 8, 16}, 40]

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).

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).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula