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A054519
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Number of increasing arithmetic progressions ending in n (in the nonnegative integers), including those of length 1 or 2.
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8
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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]
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
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FORMULA
| a(n) = A051336(n+1)-A051336(n) = a(n-1)+A000005(n) = A006218(n)+1.
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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.
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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]
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CROSSREFS
| Cf. A000005, A006218, A051336. Left edge of A056535.
Sequence in context: A050502 A022760 A164286 * A168434 A038107 A195526
Adjacent sequences: A054516 A054517 A054518 * A054520 A054521 A054522
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Apr 07 2000
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