A083295 -id:A083295 - cp's OEIS frontend

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

Paul Barry, Apr 24 2003

Binomial transform of A083295.

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

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (-4,21).

Cf. A083295, A083297.

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

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 *)

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 */

a(n)=(4*3^n+(-7)^n)/5 \\ Charles R Greathouse IV, Oct 07 2015

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

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

A083294 a(n) = (4 + (-9)^n)/5.

Original entry on oeis.org

1, -1, 17, -145, 1313, -11809, 106289, -956593, 8609345, -77484097, 697356881, -6276211921, 56485907297, -508373165665, 4575358490993, -41178226418929, 370604037770369, -3335436339933313, 30018927059399825, -270170343534598417, 2431533091811385761

Offset: 0

Paul Barry, Apr 24 2003

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (-8,9).

Cf. A083295.

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

(4+(-9)^Range[0,20])/5 (* or *) LinearRecurrence[{-8,9},{1,-1},30] (* Harvey P. Dale, Sep 25 2021 *)

a(n) = (4 + (-9)^n)/5.
G.f.: (1+7*x)/((1-x)*(1+9*x)).
E.g.f.: (4*exp(x) + exp(-9*x))/5.

cp's OEIS Frontend

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

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