A131064 Binomial transform of [1, 1, 5, 5, 5, ...].

1, 2, 8, 24, 60, 136, 292, 608, 1244, 2520, 5076, 10192, 20428, 40904, 81860, 163776, 327612, 655288, 1310644, 2621360, 5242796, 10485672, 20971428, 41942944, 83885980, 167772056, 335544212, 671088528, 1342177164, 2684354440

Offset

0,2

Comments

Row sums of triangle A131063. - Emeric Deutsch, Jun 20 2007

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

From Emeric Deutsch, Jun 20 2007: (Start)

a(n) = 5*2^n - 4*(n + 1).

G.f.: (1-2*x+5*x^2)/((1-2*x)*(1-x)^2). (End)

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). - Vincenzo Librandi, Jul 05 2012

E.g.f.: 5*exp(2*x) - 4*(1+x)*exp(x). - G. C. Greubel, Mar 12 2020

Example

a(3) = 24 = sum of row 4 terms of A131063: (1 + 11 + 11 + 1).
a(3) = 24 = (1, 3, 3, 1) dot (1, 1, 5, 5).

Maple

a := proc (n) options operator, arrow; 5*2^n-4*n-4 end proc: seq(a(n), n = 0 .. 30); # Emeric Deutsch, Jun 20 2007

Mathematica

CoefficientList[Series[(1-2x+5x^2)/((1-2x)(1-x)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 05 2012 *)
LinearRecurrence[{4, -5, 2}, {1, 2, 8}, 30] (* Harvey P. Dale, Dec 29 2014 *)

Prog

(Magma) I:=[1, 2, 8]; [n le 3 select I[n] else 4*Self(n-1)-5*Self(n-2) + 2*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jul 05 2012
(GAP) Print(List([0..30], n->5*2^n-4*n-4)); # Muniru A Asiru, Feb 21 2019
(Sage) [5*2^n -4*(n+1) for n in (0..30)] # G. C. Greubel, Mar 12 2020

Crossrefs

Cf. A109128, A123203, A131060, A131061, A131063, A131065, A131066, A131067, A131068.

Sequence in context: A083553 A051745 A006734 * A263598 A075218 A006728

Adjacent sequences: A131061 A131062 A131063 * A131065 A131066 A131067

Keyword

nonn,easy

Author

Gary W. Adamson, Jun 13 2007

Extensions

Corrected and extended by Emeric Deutsch, Jun 20 2007

Status

approved