|
| |
|
|
A005711
|
|
a(n)=a(n-1)+a(n-9).
(Formerly M0479)
|
|
9
| |
|
|
1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 19, 24, 30, 37, 45, 54, 64, 76, 91, 110, 134, 164, 201, 246, 300, 364, 440, 531, 641, 775, 939, 1140, 1386, 1686, 2050, 2490, 3021, 3662, 4437, 5376, 6516, 7902, 9588, 11638, 14128, 17149, 20811, 25248
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,9
|
|
|
REFERENCES
| Problem E3274, Amer. Math. Monthly, 95 (1988), 555.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
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.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 382
|
|
|
FORMULA
| G.f.: (1+x^8)/(1-x-x^9).
For positive integers n and k such that k <= n <= 9*k, and 8 devides n-k, define c(n,k) = binomial(k,(n-k)/8), and c(n,k) = 0, otherwise. Then, for n>= 1, a(n-1) = sum(c(n,k), k=1..n). - Milan Janjic, Dec 09 2011
|
|
|
MAPLE
| A005711:=-(1+z**8)/(-1+z+z**9); [S. Plouffe in his 1992 dissertation.]
ZL:=[S, {a = Atom, b = Atom, S = Prod(X, Sequence(Prod(X, b))), X = Sequence(b, card >= 8)}, unlabelled]: seq(combstruct[count](ZL, size=n), n=9..65); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 26 2008
M := Matrix(9, (i, j)-> if j=1 and member(i, [1, 9]) then 1 elif (i=j-1) then 1 else 0 fi); a := n -> (M^(n+1))[1, 1]; seq (a(n), n=0..56); - Alois P. Heinz, Jul 27 2008
|
|
|
MATHEMATICA
| LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1}, 80] (* From Vladimir Joseph Stephan Orlovsky, Feb 16 2012 *)
|
|
|
PROG
| (PARI) x='x+O('x^66); Vec((1+x^8)/(1-x-x^9)) /* Joerg Arndt, Jun 25 2011 */
|
|
|
CROSSREFS
| Cf. A005710.
Sequence in context: A101170 A130224 A017903 * A059765 A180479 A193456
Adjacent sequences: A005708 A005709 A005710 * A005712 A005713 A005714
|
|
|
KEYWORD
| nonn,easy,changed
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Mohammad K. Azarian, azarian(AT)evansville.edu
|
| |
|
|
