proposed

approved

editing

proposed

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

a(n) ~ (9/4)*(sqrt(5)-12)*fibonacci(n).

a(n) = (9/2)*fibonacci(n) + (-1)^n - sqrt(3)*sin(n*Pi/3).

<a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,1,1).

signature (1,1,-1,1,1).

The second upper subdiagonal (4, 8, 7, 14, 19, 38, 67, ...) is not in the OEIS.

<a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>,

signature (1,1,-1,1,1).

Cf. A000079, A153130, A185346, A254076.

allocated for Jean-François Alcover

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

0,2

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, 67, ...) 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).

G.f.: (1+x+x^2+3*x^3+5*x^4) / (1-x-x^2+x^3-x^4-x^5).

a(n) ~ (9/4)*(sqrt(5)-1)*fibonacci(n).

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

allocated

nonn,easy

Jean-François Alcover and Paul Curtz, Oct 29 2017

approved

editing

allocated for Jean-François Alcover

allocated

approved