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Search: id:A145018
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| A145018 |
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a(1) = 4; then add 1 to the first number, then 2, then 3 and so on. |
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+0
2
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| 4, 5, 7, 10, 14, 19, 25, 32, 40, 49, 59, 70, 82, 95, 109, 124, 140, 157, 175, 194, 214, 235, 257, 280, 304, 329, 355, 382, 410, 439, 469, 500, 532, 565, 599, 634, 670, 707, 745, 784, 824, 865, 907, 950, 994, 1039, 1085, 1132, 1180, 1229, 1279, 1330, 1382, 1435, 1489, 1544, 1600, 1657, 1715, 1774, 1834, 1895, 1957, 2020, 2084, 2149, 2215
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Except for the first term, if a(1)=5, a(n)=a(n-1)+n [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 07 2009]
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FORMULA
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a(n)=(n^2-n+8)/2. - Benoit Cloitre.
G.f.: x(4-7x+4x^2)/(1-x)^3. a(n)=a(n-1)+n-1 = 4+A000217(n-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 01 2008
a(n) =4+C(n,2), n>=1. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 12 2009]
a(n)=n+a(n-1)-1 (with a(1)=4) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 07 2009]
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EXAMPLE
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For n=2, a(2)=2+4-1=5; n=3, a(3)=3+5-1=7; n=4, a(4)=4+7-1=10 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 07 2009]
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MATHEMATICA
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i=0; s=4; lst={}; Do[s+=n+i; AppendTo[lst, s], {n, 0, 4!, 1}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 30 2008]
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PROGRAM
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(PARI) a(n) = 10+1/2*n^2-7/2*n j=[]; for(n=4, 34, j=concat(j, a(n))); j = [4, 5, 7, 10, 14, 19, 25, 32, 40, 49, 59, 70, 82, 95, 109, 124, 140, 157, 175, 194, 214, 235, 257, 280, 304, 329, 355, 382, 410, 439, 469] [From Alexander R. Povolotsky (pevnev(AT)juno.com), Sep 29 2008]
(Other) SAGE:[4+binomial(n, 2) for n in xrange(1, 68)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 12 2009]
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CROSSREFS
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Sequence in context: A013951 A013947 A093517 this_sequence A018910 A022936 A057496
Adjacent sequences: A145015 A145016 A145017 this_sequence A145019 A145020 A145021
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KEYWORD
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nonn
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AUTHOR
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Jayanth (mergujayanth(AT)yahoo.com), Sep 29 2008
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EXTENSIONS
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More terms from Alexander R. Povolotsky (pevnev(AT)juno.com), Sep 29 2008
Edited by Benoit Cloitre (benoit7848c(AT)orange.fr) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 30 2008
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