OFFSET
0,2
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).
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)
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]
PROG
(Python)
print([[1, 11, -29, -189][n%4] + [450, 3000, -7200, -48000][n%4]*(256**(n//4)-1)//255 for n in range(24)])
(PARI) Vec((1 - 2*x)*(1 + 12*x) / ((1 - x)*(1 + 16*x^2)) + O(x^30)) \\ Colin Barker, Feb 07 2017
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Andrey Zabolotskiy, Feb 06 2017
STATUS
approved