A083223 -id:A083223 - 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

A083224 a(n) = (6*7^n + (-7)^n)/7.

Original entry on oeis.org

1, 5, 49, 245, 2401, 12005, 117649, 588245, 5764801, 28824005, 282475249, 1412376245, 13841287201, 69206436005, 678223072849, 3391115364245, 33232930569601, 166164652848005, 1628413597910449, 8142067989552245

Offset: 0

Paul Barry, Apr 23 2003

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (0,49).

Cf. A083223, A083225.

[(6*7^n+(-7)^n)/7: n in [0..25]]; // Vincenzo Librandi, Jun 29 2011

LinearRecurrence[{0,49},{1,5},30] (* Harvey P. Dale, Oct 12 2018 *)

a(n) = (6*7^n + (-7)^n)/7.
G.f.: (1+5*x)/((1+7*x)*(1-7*x)).
E.g.f.: (6*exp(7*x) + exp(-7*x))/7.

cp's OEIS Frontend

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

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