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

Author

Paul Barry, Apr 24 2003

Keywords

• sign
• easy

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).

Crossrefs

Cf. A083295, A083297.

Programs

Magma

[(4*3^n+(-7)^n)/5: n in [0..30]]; // Vincenzo Librandi, Jun 08 2011

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 *)

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

Formula

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

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