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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007502 Les Marvin sequence: a(n) = F(n)+(n-1)*F(n-1), F() = Fibonacci numbers.
(Formerly M1170)
7
1, 2, 4, 9, 17, 33, 61, 112, 202, 361, 639, 1123, 1961, 3406, 5888, 10137, 17389, 29733, 50693, 86204, 146246, 247577, 418299, 705479, 1187857, 1997018, 3352636, 5621097, 9412937, 15744681, 26307469, 43912648 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Denominators of convergents of the continued fraction with the n partial quotients: [1;1,1,...(n-1 1's)...,1,n], starting with [1], [1;2], [1;1,3], [1;1,1,4], ... Numerators are A088209(n-1). - Paul D. Hanna, Sep 23 2003

REFERENCES

Les Marvin, Problem, J. Rec. Math., Vol. 10 (No. 3, 1976-1977), p. 213.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..500

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

FORMULA

G.f.: (1-x^2+x^3)/(1-x-x^2)^2. - Paul D. Hanna, Sep 23 2003

a(n+1) = A109754(n, n+1) = A101220(n, 0, n+1).  - N. J. A. Sloane, May 19 2006

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4) for n>3, a(0)=1, a(1)=2, a(2)=4, a(3)=9. - Harvey P. Dale, Jul 13 2011

EXAMPLE

a(7) = F(7)+6*F(6) = 13+6*8 = 61.

MATHEMATICA

Table[Fibonacci[n]+(n-1)*Fibonacci[n-1], {n, 40}] (* or *) LinearRecurrence[ {2, 1, -2, -1}, {1, 2, 4, 9}, 40](* Harvey P. Dale, Jul 13 2011 *)

f[n_] := Denominator@  FromContinuedFraction@ Join[ Table[1, {n}], {n + 1}]; Array[f, 30, 0] (* Robert G. Wilson v, Mar 04 2012 *)

PROG

(Haskell)

a007502 n = a007502_list !! (n-1)

a007502_list = zipWith (+) a045925_list $ tail a000045_list

-- Reinhard Zumkeller, Oct 01 2012, Mar 04 2012

(PARI) Vec((1-x^2+x^3)/(1-x-x^2)^2+O(x^99)) \\ Charles R Greathouse IV, Mar 04, 2012

CROSSREFS

Cf. A088209 (numerators) , A000045, A109754, A101220.

Cf. A045925.

Sequence in context: A192967 A182806 A302832 * A088039 A266108 A077931

Adjacent sequences:  A007499 A007500 A007501 * A007503 A007504 A007505

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 18 07:00 EDT 2018. Contains 316307 sequences. (Running on oeis4.)