|
Search: id:A005230
|
|
|
| A005230 |
|
Stern's sequence: a(1) = 1, a(n+1) is the sum of the m preceding terms, where m*(m-1)/2 < n <= m*(m+1)/2 or equivalently m = ceil((sqrt(8*n+1)-1)/2) = A002024(n).
(Formerly M0785)
|
|
+0
7
|
|
| 1, 1, 2, 3, 6, 11, 20, 40, 77, 148, 285, 570, 1120, 2200, 4323, 8498, 16996, 33707, 66844, 132568, 262936, 521549, 1043098, 2077698, 4138400, 8243093, 16419342, 32706116, 65149296, 130298592, 260075635, 519108172, 1036138646, 2068138892, 4128034691
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
REFERENCES
|
Kreweras, G.; Sur quelques problemes relatifs au vote pondere, [ Some problems of weighted voting ] Math. Sci. Humaines No. 84 (1983), 45-63.
M. A. Stern, Aufgaben, J. Reine Angew. Math., 18 (1838), 100.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n = 1..200
Index entries for sequences related to Stern's sequences
Index entries for "core" sequences
|
|
FORMULA
|
Partial sums give Conway-Guy sequence A005318. Cf. A066777.
2*a(n*(n+1)/2 + 1) = a(n*(n+1)/2 + 2) for n>=1; limit_{n->infty} a(n+1)/a(n) = 2. - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 28 2006
|
|
MAPLE
|
A005230[1] := 1: n := 50: for k from 1 to n-1 do: A005230[k+1] := sum('A005230[j]', 'j'=k+1-(ceil((sqrt(8*k+1)-1)/2))..k): od: [seq(A005230[k], k=1..n)];
|
|
PROGRAM
|
(PARI) a(n)=if(n==1, 1, sum(k=1, ceil((sqrt(8*n-7)-1)/2), a(n-k))) - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 28 2006
|
|
CROSSREFS
|
Sequence in context: A115792 A054177 A096080 this_sequence A030037 A077078 A077079
Adjacent sequences: A005227 A005228 A005229 this_sequence A005231 A005232 A005233
|
|
KEYWORD
|
core,easy,nonn,nice
|
|
AUTHOR
|
njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
|
|
EXTENSIONS
|
Description corrected by Mario Szegedy Sep 15 1996; and revised with Maple code by UlrSchimke(AT)aol.com, Mar 16, 2002
|
|
|
Search completed in 0.002 seconds
|
