A048478 a(n) = T(6,n), array T given by A048472.

1, 8, 29, 85, 225, 561, 1345, 3137, 7169, 16129, 35841, 78849, 172033, 372737, 802817, 1720321, 3670017, 7798785, 16515073, 34865153, 73400321, 154140673, 322961409, 675282945, 1409286145, 2936012801, 6106906625, 12683575297, 26306674689, 54492397569

Offset

0,2

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (7, 14, 21, ...).

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) = 7*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+3*x-3*x^2)/((1-x)*(1-2*x)^2). (End)

E.g.f.: exp(x)*(1 + 7*x*exp(x)). - Elmo R. Oliveira, Oct 30 2025

Prog

(Magma) [7*n * 2^(n-1) + 1: n in [0..30]]; // Vincenzo Librandi, Sep 23 2011
(PARI) Vec((1+3*x-3*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ Colin Barker, Feb 18 2016

Crossrefs

Cf. A048472.

Sequence in context: A333510 A055536 A131438 * A001360 A294838 A116952

Adjacent sequences: A048475 A048476 A048477 * A048479 A048480 A048481

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved