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Search: id:A084849
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| 1, 4, 11, 22, 37, 56, 79, 106, 137, 172, 211, 254, 301, 352, 407, 466, 529, 596, 667, 742, 821, 904, 991, 1082, 1177, 1276, 1379, 1486, 1597, 1712, 1831, 1954, 2081, 2212, 2347, 2486, 2629, 2776, 2927, 3082, 3241, 3404, 3571, 3742, 3917, 4096, 4279, 4466
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)=A058331(n)+A000027(n).
a(n) = A014105(n) + 1; A100035(a(n)) = 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 31 2004
Equals (1, 2, 3,...) convolved with (1, 2, 4, 4, 4,...). a(3) = 22 = (1, 2, 3, 4) dot (4, 4, 2, 1) = (4 + 8 + 6 + 4). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 01 2009]
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FORMULA
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G.f.: (1+x+2x^2)/(1 - x)^3.
a(n)=ceiling((2n+1)^2/2)-n=A001844(n)-n; - Paul Barry (pbarry(AT)wit.ie), Jul 16 2006
Row sums of triangle A131901. A084849 = binomial transform of (1, 3, 4, 0, 0, 0,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 26 2007
Equals A134082 * [1,2,3,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 07 2007
a(n)=4*n+a(n-1)-5 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
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EXAMPLE
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For n=2, a(2)=4*2+1-5=4; n=3, a(3)=4*3+4-5=11; n=4, a(4)=4*4+11-5=22 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
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MATHEMATICA
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s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 200, 4}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
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CROSSREFS
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Cf. A100040, A100041, A100036, A100037, A100038, A100039.
Cf. A131901.
Cf. A134082.
Sequence in context: A038414 A008154 A008162 this_sequence A008265 A160424 A008229
Adjacent sequences: A084846 A084847 A084848 this_sequence A084850 A084851 A084852
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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), Jun 09 2003
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