A053455 a(n) = ((8^n) - (-6)^n)/14.
0, 1, 2, 52, 200, 2896, 15392, 169792, 1078400, 10306816, 72376832, 639480832, 4753049600, 40201179136, 308548739072, 2546754076672, 19903847628800, 162051890937856, 1279488468058112, 10337467701133312, 82090381869056000, 660379213392510976, 5261096756499709952, 42220395755839946752
Offset: 0
References
- A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (2,48).
Programs
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Maple
A053455:=n->((8^n)-(-6)^n)/14; seq(A053455(n), n=0..30); # Wesley Ivan Hurt, Mar 07 2014
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Mathematica
LinearRecurrence[{2,48},{1,2},30] (* Harvey P. Dale, Nov 28 2011 *) CoefficientList[Series[x / (1 - 2 x - 48 x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Mar 08 2014 *) -
PARI
a(n) = ((8^n)-(-6)^n)/14; \\ Joerg Arndt, Mar 08 2014
Formula
a(n) = 2*a(n-1) + 48*a(n-2), n>=2; a(0)=0, a(1)=1.
a(n) = ((8^n)-(-6)^n)/14 = (2^(n-1))*((4^n) - (-3)^n)/7 = 2^(n-1)*A053404(n).
G.f.: x/((1+6*x)*(1-8*x)). - Harvey P. Dale, Nov 28 2011
a(n) = A080921(n). - Philippe Deléham, Mar 05 2014
a(n+1) = Sum_{k=0..n} A238801(n,k)*7^k. - Philippe Deléham, Mar 07 2014
Extensions
More terms from James Sellers, Feb 02 2000
New name (from formula), Joerg Arndt, Mar 05 2014
Comments