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A062092 a(n) = 2*a(n-1)-(-1)^n for n>0, a(0)=2. 11
2, 5, 9, 19, 37, 75, 149, 299, 597, 1195, 2389, 4779, 9557, 19115, 38229, 76459, 152917, 305835, 611669, 1223339, 2446677, 4893355, 9786709, 19573419, 39146837, 78293675, 156587349, 313174699, 626349397, 1252698795, 2505397589 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Let A be the Hessenberg matrix of order n, defined by: A[1,j]=A[i,i]:=1, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=charpoly(A,3). - Milan Janjic, Jan 24 2010

REFERENCES

T. Koshy, Fibonacci and Lucas numbers with applications, Wiley, 2001, p. 98.

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (1,2).

FORMULA

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

a(n) = 2^(n+1) + A001045(n).

A002487(a(n)) = A000032(n+1).

G.f.: (2+3*x)/(1-x-2*x^2).

E.g.f.: (7*exp(2*x)-exp(-x))/3.

Running sum of 3 consecutive elements of Jacobsthal sequence A001045(n): a(n) = A001045(n) + A001045(n-1) + A001045(n-2). - Alexander Adamchuk, May 16 2006

EXAMPLE

a(4) = 37 hence a(5) = 2*37 + 1=75 and a(6) = 2*75 - 1 = 149.

MATHEMATICA

LinearRecurrence[{1, 2}, {2, 5}, 40] (* Jean-François Alcover, Aug 02 2021 *)

PROG

(PARI) a(n) = (7*2^n - (-1)^n)/3; \\ Harry J. Smith, Aug 01 2009

CROSSREFS

Cf. A001045.

Sequence in context: A122893 A178841 A214319 * A320172 A079117 A030137

Adjacent sequences:  A062089 A062090 A062091 * A062093 A062094 A062095

KEYWORD

nonn,easy

AUTHOR

Amarnath Murthy, Jun 16 2001

EXTENSIONS

More terms from Jason Earls, Jun 18 2001

Additional comments from Michael Somos, Jun 24 2002

STATUS

approved

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Last modified September 18 23:16 EDT 2021. Contains 347548 sequences. (Running on oeis4.)