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A140766
a(n) = 6*a(n-1) - 6*a(n-2).
2
1, 5, 24, 114, 540, 2556, 12096, 57240, 270864, 1281744, 6065280, 28701216, 135815616, 642686400, 3041224704, 14391229824, 68100030720, 322252805376, 1524916647936, 7215983055360, 34146398444544, 161582492335104, 764616563343360, 3618204426049536
OFFSET
1,2
COMMENTS
Companion sequence = A030192 beginning (1, 6, 30, 144, 684,...).
FORMULA
a(n) = 6*a(n-1) - 6*a(n-2); a(1) = 1, a(2) = 5.
Term (1,1) of M^n, where M = the 3x3 matrix [1,1,1; 1,2,1; 3,1,3].
O.g.f.: x(1-x)/(1-6x+6x^2). a(n)=A030192(n-1)-A030192(n-2). - R. J. Mathar, May 31 2008
a(n) = Sum_{1<=k<=n} A030523(n,k)*2^(k-1). - Philippe Deléham, Feb 19 2013
EXAMPLE
a(5) = 540 = 6*a(4) - 6*a(3) = 6*(114) - 6*24.
a(5) = 540 = term (1,1) of X^5.
MATHEMATICA
LinearRecurrence[{6, -6}, {1, 5}, 30] (* Harvey P. Dale, Oct 01 2014 *)
CROSSREFS
Sequence in context: A347029 A141223 A289783 * A026388 A242509 A057969
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from R. J. Mathar, May 31 2008
More terms from Harvey P. Dale, Oct 01 2014
STATUS
approved