A092900 A Jacobsthal sequence (A078008) to base 4.

1, 0, 2, 2, 12, 22, 112, 222, 1112, 2222, 11112, 22222, 111112, 222222, 1111112, 2222222, 11111112, 22222222, 111111112, 222222222, 1111111112, 2222222222, 11111111112, 22222222222, 111111111112, 222222222222, 1111111111112

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,11,0,-10).

Formula

For n > 0, a(2*n+1) is represented as a string of n 2's and a(2*n) as a string of (n-1) 1's followed by a 2.

From Colin Barker, Apr 01 2016: (Start)

a(n) = (6+10*(-1)^n+10^(1/2*(-1+n))*(2-2*(-1)^n+sqrt(10)+(-1)^n*sqrt(10)))/18.

a(n) = (10^(n/2)+8)/9 for n even.

a(n) = (2^((n+1)/2)*5^((n-1)/2)-2)/9 for n odd.

a(n) = 11*a(n-2)-10*a(n-4) for n>3.

G.f.: (1-9*x^2+2*x^3) / ((1-x)*(1+x)*(1-10*x^2)).

(End)

Example

a(8)= 1112 because A078008(8) = 86 (in base 10) = 64 + 16 + 4 + 2 = 1*(4^3) + 1*(4^2) + 1*(4^1) + 2.

Prog

(PARI) Vec((1-9*x^2+2*x^3)/((1-x)*(1+x)*(1-10*x^2)) + O(x^30)) \\ Colin Barker, Apr 01 2016

Crossrefs

Cf. A081857.

Sequence in context: A202669 A178845 A140431 * A303537 A369086 A355871

Adjacent sequences: A092897 A092898 A092899 * A092901 A092902 A092903

Keyword

easy,base,nonn

Author

Paul Barry, Mar 12 2004

Status

approved