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Search: id:A080827
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| A080827 |
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Rounded up staircase on natural numbers. |
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+0
3
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| 1, 3, 5, 9, 13, 19, 25, 33, 41, 51, 61, 73, 85, 99, 113, 129, 145, 163, 181, 201, 221, 243, 265, 289, 313, 339, 365, 393, 421, 451, 481, 513, 545, 579, 613, 649, 685, 723, 761, 801, 841, 883, 925, 969, 1013, 1059, 1105, 1153, 1201, 1251, 1301, 1353, 1405, 1459
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Represents the 'rounded up' staircase diagonal on A000027, arranged as a square array. A000982 is the 'rounded down' staircase.
a(1)= 1, a(2n) = a(2n-1) + 2n, a(2n+1) = a(2n) +2n. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 07 2003
Partial sums of A131055. - Paul Barry (pbarry(AT)wit.ie), Jun 14 2008
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FORMULA
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a(n)=Ceiling((n^2+1)/2)
G.f.: (1+x-x^2+x^3)/((1+x)(1-x)^3); a(n)=(n+1)(n+2)/2-floor(n/2); - Paul Barry (pbarry(AT)wit.ie), Apr 12 2008
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MATHEMATICA
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s1=0; lst={}; Do[s1+=n; If[EvenQ[s1], s1-=1]; AppendTo[lst, s1], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 06 2009]
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CROSSREFS
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Apart from leading term, identical to A099392.
Sequence in context: A065802 A118028 A099392 this_sequence A102378 A118026 A108754
Adjacent sequences: A080824 A080825 A080826 this_sequence A080828 A080829 A080830
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 28 2003
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