|
| |
|
|
A062544
|
|
n plus sum of previous three terms.
|
|
5
| |
|
|
0, 1, 3, 7, 15, 30, 58, 110, 206, 383, 709, 1309, 2413, 4444, 8180, 15052, 27692, 50941, 93703, 172355, 317019, 583098, 1072494, 1972634, 3628250, 6673403, 12274313, 22575993, 41523737, 76374072, 140473832, 258371672, 475219608
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| It appears that this is the number of nonempty subsets of {1,2,...,n} with no gap of length greater than 3 (a set S has a gap of length d if a and b are in S but no x with a<x<b is in S, where b-a=d). See A119407 for the corresponding problem for gaps of length 4. - John W. Layman, Nov 02 2011
|
|
|
LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,300
|
|
|
FORMULA
| a(n) = +3*a(n-1) -2*a(n-2) -1*a(n-4) +1*a(n-5) [Joerg Arndt, Apr 2 2011]
a(n) =n+a(n-1)+a(n-2)+a(n-3) =(A001590(n+4)-n-3)/2
|
|
|
EXAMPLE
| a(5)=5+15+7+3=30
|
|
|
MATHEMATICA
| Join[{c=0}, a=b=0; Table[z=b+a+c+n; a=b; b=c; c=z, {n, 1, 40}]] (*From Vladimir Joseph Stephan Orlovsky, Apr 02 2011*)
|
|
|
PROG
| (PARI) { a=a1=a2=a3=0; for (n=0, 300, write("b062544.txt", n, " ", a+=n + a2 + a3); a3=a2; a2=a1; a1=a ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 08 2009]
|
|
|
CROSSREFS
| n plus sum of all previous terms gives A000225, n plus sum of two previous terms gives A001924, n plus previous term gives A000217, n gives A001477.
Cf. A007800.
Cf. A119407.
Sequence in context: A187100 A182726 A023610 * A120411 A069112 A064084
Adjacent sequences: A062541 A062542 A062543 * A062545 A062546 A062547
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jun 26 2001
|
| |
|
|
