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A092900 A Jacobsthal sequence (A078008) to base 4. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A164961 A122007 A137782

Adjacent sequences:  A092897 A092898 A092899 * A092901 A092902 A092903

KEYWORD

easy,base,nonn

AUTHOR

Paul Barry, Mar 12 2004

STATUS

approved

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Last modified March 27 12:31 EDT 2017. Contains 284176 sequences.