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Search: id:A082111
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| 1, 7, 15, 25, 37, 51, 67, 85, 105, 127, 151, 177, 205, 235, 267, 301, 337, 375, 415, 457, 501, 547, 595, 645, 697, 751, 807, 865, 925, 987, 1051, 1117, 1185, 1255, 1327, 1401, 1477, 1555, 1635, 1717, 1801, 1887, 1975, 2065, 2157, 2251, 2347, 2445, 2545, 2647
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 29 2009: (Start)
Let (a,b) = roots to x^2 -5x + 1 = 0 = 4.79128... and .208712...
Then a(n) = (n + a) * (n + b). Example: a(5) = 51 = (5 + 4.79128...) * (5 + .208712...) (End)
Except for the first term, a(n)=2*n+a(n-1)+4 (with a(1)=7) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
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FORMULA
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a(n)=n^2+5n+1
a(n)=2*n+a(n-1)+2 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 29 2009]
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EXAMPLE
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For n=2, a(2)=2*2+1+2=7; n=3, a(3)=2*3+7+2=15; n=4, a(4)=2*4+15+2=25 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 29 2009]
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MAPLE
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a:=array(1...50): a[1]:=1: print(1, a[1]); for i from 2 to 50 do a[i]:= a[i-1]+(2*binomial(i+1, i)):print(i, a[i]); od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 27 2007
with (combinat):with (combinat):seq(fibonacci(3, n)+n-6, n=2..51); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2008
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MATHEMATICA
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s = 1; lst = {s}; Do[s += n + 5; AppendTo[lst, s], {n, 1, 100, 2}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
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CROSSREFS
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Cf. A028872, A028387.
Cf. A002522.
Sequence in context: A113505 A076796 A056119 this_sequence A154935 A012480 A063611
Adjacent sequences: A082108 A082109 A082110 this_sequence A082112 A082113 A082114
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KEYWORD
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easy,nonn,new
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Apr 04 2003
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