A083297 -id:A083297 - cp's OEIS frontend

A083222 a(n) = (4*5^n + (-5)^n)/5.

1, 3, 25, 75, 625, 1875, 15625, 46875, 390625, 1171875, 9765625, 29296875, 244140625, 732421875, 6103515625, 18310546875, 152587890625, 457763671875, 3814697265625, 11444091796875, 95367431640625, 286102294921875

Offset: 0

Paul Barry, Apr 23 2003

Binomial transform of A083297.

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (0,25).

Cf. A083223, A083299.

[(4*5^n+(-5)^n)/5: n in [0..25]]; // Vincenzo Librandi, Jun 29 2011

LinearRecurrence[{0,25},{1,3},30] (* or *) Riffle[NestList[25#&,1,10], NestList[ 25#&,3,10]] (* Harvey P. Dale, Dec 14 2017 *)

a(n)=(4*5^n+(-5)^n)/5 \\ Charles R Greathouse IV, Jun 29 2011

a(n) = (4*5^n + (-5)^n)/5.
G.f.: (1+3*x)/((1+5*x)(1-5*x)).
E.g.f.: (4*exp(5*x) + exp(-5*x))/5.

Edited by N. J. A. Sloane, Jun 08 2007

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

Original entry on oeis.org

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.

cp's OEIS Frontend

A083222 a(n) = (4*5^n + (-5)^n)/5.

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