|
Search: id:A054519
|
|
|
| A054519 |
|
Number of increasing arithmetic progressions ending in n (in the nonnegative integers), including those of length 1 or 2. |
|
+0
8
|
|
| 1, 2, 4, 6, 9, 11, 15, 17, 21, 24, 28, 30, 36, 38, 42, 46, 51, 53, 59, 61, 67, 71, 75, 77, 85, 88, 92, 96, 102, 104, 112, 114, 120, 124, 128, 132, 141, 143, 147, 151, 159, 161, 169, 171, 177, 183
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
a(0)=1, a(n)=a(n-1) + sigma_0(n), in terms of OEIS a(n)=a(n-1)+A000005(n). [From Ctibor O. Zizka (c.zizka(AT)email.cz), Nov 08 2008]
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..1000
|
|
FORMULA
|
a(n) = A051336(n+1)-A051336(n) = a(n-1)+A000005(n) = A006218(n)+1.
|
|
EXAMPLE
|
a(3)=6 because the six increasing progressions (3), (2,3), (1,2,3), (0,1,2,3), (1,3) and (0,3) all end in 3.
|
|
MAPLE
|
IBI:= {{}}: a[0]:= 1: for n from 1 to 45 do IBI:= IBI union map(t -> t union {n}, select(t -> (t minus map(q -> n-q, t)={}), IBI)); a[n]:= nops(IBI) od: seq(a[n], n=0..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 18 2007
with(numtheory):a[1]:=2: for n from 2 to 59 do a[n]:=a[n-1]+tau(n) od: seq(a[n], n=0..45); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 21 2009]
|
|
CROSSREFS
|
Cf. A000005, A006218, A051336. Left edge of A056535.
Sequence in context: A050502 A022760 A164286 this_sequence A038107 A153196 A077220
Adjacent sequences: A054516 A054517 A054518 this_sequence A054520 A054521 A054522
|
|
KEYWORD
|
easy,nonn,nice
|
|
AUTHOR
|
Henry Bottomley (se16(AT)btinternet.com), Apr 07 2000
|
|
|
Search completed in 0.002 seconds
|
