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A117863
Number of palindromes (in base 4) below 4^n.
1
3, 6, 18, 30, 78, 126, 318, 510, 1278, 2046, 5118, 8190, 20478, 32766, 81918, 131070, 327678, 524286, 1310718, 2097150, 5242878, 8388606, 20971518, 33554430, 83886078, 134217726, 335544318, 536870910, 1342177278, 2147483646, 5368709118, 8589934590
OFFSET
1,1
FORMULA
a(n) = 5*4^((n-1)/2)-2 (n odd), 2*4^(n/2)-2 (n even).
G.f.: 3*x*(x+1) / ((x-1)*(2*x-1)*(2*x+1)). [Colin Barker, Feb 15 2013]
a(1)=3, a(2)=6, a(3)=18, a(n)=a(n-1)+4*a(n-2)-4*a(n-3). - Harvey P. Dale, May 09 2013
MATHEMATICA
Rest[CoefficientList[Series[3x (x+1)/((x-1)(2x-1)(2x+1)), {x, 0, 40}], x]] (* or *) LinearRecurrence[{1, 4, -4}, {3, 6, 18}, 40] (* Harvey P. Dale, May 09 2013 *)
CROSSREFS
Cf. A050250.
Sequence in context: A088339 A064400 A352786 * A103100 A277317 A277318
KEYWORD
nonn,base,easy
AUTHOR
Martin Renner, May 02 2006
EXTENSIONS
More terms from Colin Barker, Feb 15 2013
STATUS
approved