A083594 -id:A083594 - cp's OEIS frontend

A083595 a(n) = (7*2^n - 4(-1)^n)/3.

1, 6, 8, 20, 36, 76, 148, 300, 596, 1196, 2388, 4780, 9556, 19116, 38228, 76460, 152916, 305836, 611668, 1223340, 2446676, 4893356, 9786708, 19573420, 39146836, 78293676, 156587348, 313174700, 626349396, 1252698796, 2505397588

Offset: 0

Paul Barry, May 02 2003

Binomial transform of A083594.

Vincenzo Librandi, Table of n, a(n) for n = 0..238
Index entries for linear recurrences with constant coefficients, signature (1,2).

Cf. A082541.

[(7*2^n-4*(-1)^n)/3: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011

LinearRecurrence[{1,2},{1,6},40] (* Harvey P. Dale, Aug 13 2019 *)

a(n) = (7*2^n - 4(-1)^n)/3 .
G.f.: (1+5*x)/((1-2*x)*(1+x)).
E.g.f.: (7*exp(2*x) - 4*exp(-x))/3.

A321358 a(n) = (2*4^n + 7)/3.

Original entry on oeis.org

3, 5, 13, 45, 173, 685, 2733, 10925, 43693, 174765, 699053, 2796205, 11184813, 44739245, 178956973, 715827885, 2863311533, 11453246125, 45812984493, 183251937965, 733007751853, 2932031007405, 11728124029613, 46912496118445, 187649984473773, 750599937895085, 3002399751580333

Offset: 0

Paul Curtz, Nov 07 2018

Difference table:
3,  5, 13,  45,  173,  685,  2733, ...   (this sequence)
2,  8, 32, 128,  512, 2048,  8192, ...    A004171
6, 24, 96, 384, 1536, 6144, 24576, ...    A002023

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-4).

Cf. A010701, A010727, A020988, A083594, A002023, A004171, A155980, A171382, A193579.

a[n_]:= (2*4^n + 7)/3; Array[a, 20, 0] (* or *)
CoefficientList[Series[1/3 (7 E^x + 2 E^(4 x)), {x, 0, 20}], x]*Table[n!, {n, 0, 20}] (* Stefano Spezia, Nov 10 2018 *)

a(n) = (2*4^n + 7)/3; \\ Michel Marcus, Nov 08 2018

Vec((3 - 10*x) / ((1 - x)*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Nov 10 2018

O.g.f.: (3 - 10*x) / ((1 - x)*(1 - 4*x)). - Colin Barker, Nov 10 2018
E.g.f.: (1/3)*(7*exp(x) + 2*exp(4*x)). - Stefano Spezia, Nov 10 2018
a(n) = 5*a(n-1) - 4*a(n-2), a(0) = 3, a(1) = 5.
a(n) = 4*a(n-1) - 7, a(0) = 3.
a(n) = (2/3)*(4^n-1)/3 + 3.
a(n) = A171382(2*n) = A155980(2*n+2).
a(n) = A193579(n)/3.
a(n) = A007583(n) + 2 = A001045(2*n+1) + 2.

More terms from Michel Marcus, Nov 08 2018

cp's OEIS Frontend

A083595 a(n) = (7*2^n - 4(-1)^n)/3.

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