A282137 Expansion of (24x^2-10x-1)/(16x^3-16x^2+x-1).

1, 11, -29, -189, 451, 3011, -7229, -48189, 115651, 771011, -1850429, -12336189, 29606851, 197379011, -473709629, -3158064189, 7579354051, 50529027011, -121269664829, -808464432189, 1940314637251, 12935430915011, -31045034196029, -206966894640189

Offset: 0

Author

Andrey Zabolotskiy, Feb 06 2017

Keywords

• sign
• easy

Comments

Related to base i-1 representation of integers (Khmelnik encoding): presumably a(0) is the most common first difference of A066321 (occurs with density 1/2), a(1) is the second most common difference (density 1/4), a(2) has density 1/8, and so on; in particular, A066322 consists entirely of the terms a(n) with n>3.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,-16,16).

Crossrefs

Cf. A066321, A066322, A218723.

Programs

Mathematica

LinearRecurrence[{0,0,0,257,0,0,0,-256}, {1, 11, -29, -189, 451, 3011, -7229, -48189}, 24]
LinearRecurrence[{1, -16, 16}, {1, 11, -29}, 24]

PARI

Vec((1 - 2*x)*(1 + 12*x) / ((1 - x)*(1 + 16*x^2)) + O(x^30)) \\ Colin Barker, Feb 07 2017

Python

print([[1, 11, -29, -189][n%4] + [450, 3000, -7200, -48000][n%4]*(256**(n//4)-1)//255 for n in range(24)])

Formula

a(k+8) - 257 * a(k+4) + 256 * a(k) = 0, for k >= 0. - Altug Alkan, Feb 07 2017

G.f.: (24*x^2-10*x-1)/(16*x^3-16*x^2+x-1).

From Colin Barker, Feb 07 2017: (Start)

a(n) = (-13 + (15+25*i)*(-4*i)^n + (15-25*i)*(4*i)^n) / 17 where i=sqrt(-1).

a(n) = a(n-1) - 16*a(n-2) + 16*a(n-3) for n>2.

(End)