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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
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; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 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: A358632 A062158 A034133 * A007045 A102227 A173034
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)