A048479 a(n) = T(7,n), array T given by A048472.

1, 9, 33, 97, 257, 641, 1537, 3585, 8193, 18433, 40961, 90113, 196609, 425985, 917505, 1966081, 4194305, 8912897, 18874369, 39845889, 83886081, 176160769, 369098753, 771751937, 1610612737, 3355443201, 6979321857, 14495514625, 30064771073, 62277025793

Offset

0,2

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (8, 16, 24, ...).

Links

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

Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Formula

a(n) = 8*n * 2^(n-1) + 1.

From Colin Barker, Feb 18 2016: (Start)

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3) for n>2.

G.f.: (1+4*x-4*x^2)/((1-x)*(1-2*x)^2). (End)

a(n) = Sum_{k=0..n+2} Sum_{i=0..n+2} C(n+1,i) - C(k,i). - Wesley Ivan Hurt, Sep 21 2017

E.g.f.: exp(x)*(1 + 8*x*exp(x)). - Elmo R. Oliveira, Oct 30 2025

Mathematica

Table[8 n*2^(n - 1) + 1, {n, 0, 29}] (* or *)
CoefficientList[Series[(1 + 4 x - 4 x^2)/((1 - x) (1 - 2 x)^2), {x, 0, 29}], x] (* Michael De Vlieger, Sep 22 2017 *)

Prog

(Magma) [8*n * 2^(n-1) + 1: n in [0..30]]; // Vincenzo Librandi, Sep 23 2011
(PARI) Vec((1+4*x-4*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ Colin Barker, Feb 18 2016

Crossrefs

Cf. A048472.

Sequence in context: A201024 A228170 A112888 * A031880 A231765 A220165

Adjacent sequences: A048476 A048477 A048478 * A048480 A048481 A048482

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved