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

0,3

Comments

Previous name was: A linear recursive sequence.

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).

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

Maple

A053455:=n->((8^n)-(-6)^n)/14; seq(A053455(n), n=0..30); # Wesley Ivan Hurt, Mar 07 2014

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 *)

Prog

(PARI) a(n) = ((8^n)-(-6)^n)/14; \\ Joerg Arndt, Mar 08 2014

Crossrefs

Cf. A053404, A051958, A015441, A080921.

Sequence in context: A030264 A129742 A080921 * A297947 A298556 A298766

Adjacent sequences: A053452 A053453 A053454 * A053456 A053457 A053458

Keyword

easy,nonn

Author

Barry E. Williams, Jan 13 2000

Extensions

More terms from James A. Sellers, Feb 02 2000

New name (from formula), Joerg Arndt, Mar 05 2014

Status

approved