A131066 Binomial transform of [1, 1, 6, 6, 6, ...].

1, 2, 9, 28, 71, 162, 349, 728, 1491, 3022, 6089, 12228, 24511, 49082, 98229, 196528, 393131, 786342, 1572769, 3145628, 6291351, 12582802, 25165709, 50331528, 100663171, 201326462, 402653049, 805306228, 1610612591, 3221225322

Offset

0,2

Comments

Row sums of triangle A131065. - Emeric Deutsch, Jun 20 2007

Links

Muniru A Asiru, Table of n, a(n) for n = 0..2000

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

Formula

From Emeric Deutsch, Jun 20 2007: (Start)

a(n) = 6*2^n - 5*(n + 1).

G.f.: (1 - 2*x + 6*x^2)/((1-2*x)*(1-x)^2). (End)

E.g.f.: 6*exp(2*x) - 5*(1 + x)*exp(x). - G. C. Greubel, Mar 12 2020

a(n) = 2*a(n - 1) + 5*n - 5. - Kritsada Moomuang, Jul 03 2020

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). - Wesley Ivan Hurt, Jul 10 2020

Example

a(3) = 28 = sum of row 4 of triangle A131065: (1 + 13 + 13 + 1).
a(3) = 28 = (1, 3, 3, 1) dot (1, 1, 6, 6) = (1 + 3 + 18 + 6).

Maple

a := proc (n) options operator, arrow; 6*2^n-5*n-5 end proc: seq(a(n), n = 0 .. 30); # Emeric Deutsch, Jun 20 2007

Mathematica

Table[6*2^n -5*(n+1), {n, 0, 30}] (* G. C. Greubel, Mar 12 2020 *)

Prog

(GAP) Print(List([0..30], n->6*2^n-5*n-5)); # Muniru A Asiru, Feb 21 2019
(Magma) [6*2^n -5*(n+1): n in [0..30]]; // G. C. Greubel, Mar 12 2020
(Sage) [6*2^n -5*(n+1) for n in (0..30)] # G. C. Greubel, Mar 12 2020

Crossrefs

Cf. A109128, A123203, A131060, A131061, A131063, A131064, A131065, A131067, A131068.

Sequence in context: A121643 A353017 A183376 * A341507 A058877 A192693

Adjacent sequences: A131063 A131064 A131065 * A131067 A131068 A131069

Keyword

nonn

Author

Gary W. Adamson, Jun 13 2007

Extensions

Corrected and extended by Emeric Deutsch, Jun 20 2007

Status

approved