|
Search: id:A001655
|
|
|
| A001655 |
|
Fibonomial coefficients: F(n)F(n+1)F(n+2)/2, where F() = Fibonacci numbers A000045.
(Formerly M2988 N1208)
|
|
+0
8
|
|
| 1, 3, 15, 60, 260, 1092, 4641, 19635, 83215, 352440, 1493064, 6324552, 26791505, 113490195, 480752895, 2036500788, 8626757644, 36543528780, 154800876945, 655747029795, 2777789007071, 11766903040368, 49845401197200
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
A. Brousseau, A sequence of power formulas, Fib. Quart., 6 (1968), 81-83.
A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 74.
|
|
LINKS
|
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
|
|
FORMULA
|
G.f.: (1 + x - x^2 )^-1 (1 - 4x - x^2 )^-1.
G.f.: 1/(1-3*x-6*x^2+3*x^3+x^4) = 1/((1+x-x^2)*(1-4*x-x^2)) (see Comments to A055870). a(n)=A010048(n+3, 3)= fibonomial(n+3, 3). Recursion: a(n)= 4*a(n-1)+a(n-2)+((-1)^n)*F(n+1), n >= 2; a(0)=1, a(1)=3.
|
|
MAPLE
|
A001655:=1/(z**2-z-1)/(z**2+4*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
|
|
CROSSREFS
|
Equals 1/2 * A065563(n).
First differences are in A066258.
Adjacent sequences: A001652 A001653 A001654 this_sequence A001656 A001657 A001658
Sequence in context: A036750 A058748 A049314 this_sequence A128237 A058749 A072336
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
njas
|
|
|
Search completed in 0.002 seconds
|
