A083296 a(n) = (4*3^n + (-7)^n)/5.

1, 1, 17, -47, 545, -3167, 24113, -162959, 1158209, -8054975, 56542289, -395323631, 2768682593, -19376526623, 135648440945, -949500822863, 6646620551297, -46525999485311, 325683029518481, -2279778107265455, 15958456048949921, -111709164448374239

Offset

0,3

Comments

Binomial transform of A083295.

References

K. H. Rosen, Handbook of Discrete and Combinatorial Mathematics, CRC Press LLC, 2000, p. 182 (example 9).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (-4,21).

Formula

G.f.: (1+5*x)/((1-3*x)*(1+7*x)).

E.g.f.: (4*exp(3*x) + exp(-7*x))/5.

Mathematica

Table[[(4*3^n+(-7)^n)/5], {n, 0, 21}] (* Bruno Berselli, Dec 06 2011 *)
LinearRecurrence[{-4, 21}, {1, 1}, 30] (* Harvey P. Dale, Dec 13 2015 *)

Prog

(Magma) [(4*3^n+(-7)^n)/5: n in [0..30]]; // Vincenzo Librandi, Jun 08 2011
(Maxima) a[0]:1$ a[1]:1$ a[n]:=-4*a[n-1]+21*a[n-2]$ makelist(a[n], n, 0, 21);  /* _Bruno Berselli, Dec 06 2011 */
(PARI) a(n)=(4*3^n+(-7)^n)/5 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A083295, A083297.

Sequence in context: A229448 A155841 A147058 * A362480 A159850 A031122

Adjacent sequences: A083293 A083294 A083295 * A083297 A083298 A083299

Keyword

sign,easy

Author

Paul Barry, Apr 24 2003

Status

approved