|
Search: id:A017899
|
|
|
| A017899 |
|
Expansion of 1/(1 - x^5 - x^6 - ...). |
|
+0
4
|
|
| 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 8, 11, 15, 20, 26, 34, 45, 60, 80, 106, 140, 185, 245, 325, 431, 571, 756, 1001, 1326, 1757, 2328, 3084, 4085, 5411, 7168, 9496, 12580, 16665, 22076, 29244, 38740, 51320, 67985, 90061, 119305, 158045
(list; graph; listen)
|
|
|
OFFSET
|
0,11
|
|
|
COMMENT
|
A Lam{\'e} sequence of higher order.
|
|
REFERENCES
|
J. Hermes, Anzahl der Zerlegungen einer ganzen rationalen Zahl in Summanden, Math. Ann., 45 (1894), 371-380.
|
|
FORMULA
|
G.f.: (1-x)/(1-x-x^5).
G.f.: (x-1)/(x-1+x^5). [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008]
|
|
MAPLE
|
f := proc(r) local t1, i; t1 := []; for i from 1 to r do t1 := [op(t1), 0]; od: for i from 1 to r+1 do t1 := [op(t1), 1]; od: for i from 2*r+2 to 50 do t1 := [op(t1), t1[i-1]+t1[i-1-r]]; od: t1; end; # set r = order
(Maple) a := n -> (Matrix(5, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 0$3, 1][i] else 0 fi)^n)[5, 5]; seq (a(n), n=0..50); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008]
|
|
CROSSREFS
|
For Lam{\'e} sequences of orders 1 through 9 see A000045, A000930, A017898-A017904.
Apart from initial terms, same as A003520.
Sequence in context: A060967 A026483 A098131 this_sequence A003520 A101915 A022468
Adjacent sequences: A017896 A017897 A017898 this_sequence A017900 A017901 A017902
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.002 seconds
|
