login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A033192 a(n) = binomial(Fibonacci(n) + 1, 2). 5

%I

%S 0,1,1,3,6,15,36,91,231,595,1540,4005,10440,27261,71253,186355,487578,

%T 1276003,3339820,8742471,22885995,59912931,156848616,410626153,

%U 1075018896,2814412825,7368190921,19290113571

%N a(n) = binomial(Fibonacci(n) + 1, 2).

%C a(n) = sum of n-th row in Wythoff array A003603. [_Reinhard Zumkeller_, Jan 26 2012]

%C A subsequence of the triangular numbers A000217. In fact, binomial(F(n)+1,2) = A000217(F(n)). - _M. F. Hasler_, Jan 27 2012

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-5,-1,1).

%F G.f.: x(x^3-x^2-2x+1)/[(1+x)(1-3x+x^2)(1-x-x^2)].

%F a(n) = ((Fibonacci(n)+Fibonacci(n)^2)/2). - _Gary Detlefs_ Dec 24 2010

%F A033192 = A000217 o A000045. - _M. F. Hasler_, Jan 27 2012

%F a(n) = A032441(n) - 1. - _Filip Zaludek_, Oct 30 2016

%p a:= proc(n) 1+(Matrix([[1,1], [1,0]])^n)[1,2]; %*(%-1)/2 end: seq(a(n), n=0..26); # _Alois P. Heinz_, Sep 06 2008

%t Table[Binomial[Fibonacci[n] + 1, 2], {n, 0, 50}] (* _Alonso del Arte_, Jan 26 2012 *)

%o (PARI) a(n)=binomial(fibonacci(n)+1,2) \\ _Charles R Greathouse IV_, Jan 26 2012

%Y Cf. A000045, A033191.

%K nonn,easy

%O 0,4

%A Simon Norton (simon(AT)dpmms.cam.ac.uk)

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

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 20:56 EST 2016. Contains 278895 sequences.