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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A006504 Coefficient of x^4 in (1-x-x^2)^(-n).
(Formerly M3895)
6
5, 20, 51, 105, 190, 315, 490, 726, 1035, 1430, 1925, 2535, 3276, 4165, 5220, 6460, 7905, 9576, 11495, 13685, 16170, 18975, 22126, 25650, 29575, 33930, 38745, 44051, 49880, 56265, 63240, 70840, 79101, 88060, 97755, 108225, 119510, 131651, 144690, 158670 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

G. E. Bergum and V. E. Hoggatt, Jr., Numerator polynomial coefficient array for the convolved Fibonacci sequence, Fib. Quart., 14 (1976), 43-44. (Annotated scanned copy)

G. E. Bergum and V. E. Hoggatt, Jr., Numerator polynomial coefficient array for the convolved Fibonacci sequence, Fib. Quart., 14 (1976), 43-48.

M. Janjic, Hessenberg Matrices and Integer Sequences , J. Int. Seq. 13 (2010) # 10.7.8, section 3.

P. Moree, Convoluted convolved Fibonacci numbers, arXiv:math/0311205 [math.CO], 2003.

Pieter Moree, Convoluted Convolved Fibonacci Numbers, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.2.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

FORMULA

The coefficient of x^4 in (1-x-x^2)^{-n} is the coefficient of x^4 in (1+x+2x^2+3x^3+5x^4)^n. Using the multinomial theorem one then finds that a(n)=7n/4+59*n^2/24+3*n^3/4+n^4/24. - Pieter Moree (moree(AT)mpim-bonn.mpg.de), Sep 03 2003

a(n) = n*(n+1)*(n+3)*(n+14)/4!. - Alois P. Heinz, Jan 21 2017

MAPLE

A006504:=-(5-5*z+z**2)/(z-1)**5; # Conjectured by Simon Plouffe in his 1992 dissertation.

PROG

(Haskell)

a006504 n = n * (42 + n * (59 + n * (18 + n))) `div` 24

-- Reinhard Zumkeller, Oct 16 2011

(PARI) a(n)=7*n/4+59*n^2/24+3*n^3/4+n^4/24 \\ Charles R Greathouse IV, Oct 16 2011

CROSSREFS

Row n=4 of A144064.

Sequence in context: A134481 A062158 A034133 * A007045 A102227 A173034

Adjacent sequences:  A006501 A006502 A006503 * A006505 A006506 A006507

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

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 June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)