login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A027004 a(n) = T(2*n+1,n+1), T given by A026998. 1
1, 8, 26, 73, 196, 518, 1361, 3568, 9346, 24473, 64076, 167758, 439201, 1149848, 3010346, 7881193, 20633236, 54018518, 141422321, 370248448, 969323026, 2537720633, 6643838876, 17393795998, 45537549121, 119218851368, 312119004986, 817138163593, 2139295485796 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-4,1).

FORMULA

a(n) = Fibonacci(2*n+3) + 2*Fibonacci(2*n+2) - 3.

From Colin Barker, Feb 18 2016: (Start)

a(n) = 2^(-n)*(-3*2^n-(3-sqrt(5))^n*(-2+sqrt(5))+(2+sqrt(5))*(3+sqrt(5))^n).

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

G.f.: (1+4*x-2*x^2) / ((1-x)*(1-3*x+x^2)).

(End)

PROG

(MAGMA) [Fibonacci(2*n+3) + 2*Fibonacci(2*n+2) - 3: n in [0..30]]; // Vincenzo Librandi, Apr 18 2011

(PARI) Vec((1+4*x-2*x^2)/((1-x)*(1-3*x+x^2)) + O(x^40)) \\ Colin Barker, Feb 18 2016

CROSSREFS

A002878(n+1) - 3.

Sequence in context: A296112 A051669 A207101 * A194021 A245126 A278769

Adjacent sequences:  A027001 A027002 A027003 * A027005 A027006 A027007

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 24 22:57 EST 2020. Contains 332216 sequences. (Running on oeis4.)