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Search: id:A083065
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| 1, 4, 19, 94, 469, 2344, 11719, 58594, 292969, 1464844, 7324219, 36621094, 183105469, 915527344, 4577636719, 22888183594, 114440917969, 572204589844, 2861022949219, 14305114746094, 71525573730469, 357627868652344
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OFFSET
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0,2
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COMMENT
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Inverse binomial transform of A090040=1,5,28,164,. With mentionned a(n)=5a(n-1)-1 also recurrence a(n)=6a(n-1)-5a(n-2). Linked to A131577=0,1,2,4,8,16, via submitted A154383,A154407 and A154410=10*A090040. [From Paul Curtz (bpcrtz(AT)free.fr), Jan 11 2009]
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FORMULA
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a(n)=(3*5^n+1)/4 G.f. (1-2x)/((1-5x)(1-x)) E.g.f. (3exp(5x) + exp(x))/4
a(n)=5*a(n-1)-1 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 31 2009]
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EXAMPLE
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For n=2, a(2)=5*1-1=4; n=3, a(3)=5*4-1=19; n=4, a(4)=5*19-1=94 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 31 2009]
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]*5-1 od: seq(a[n], n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008
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CROSSREFS
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Cf. A007583, A083066.
Sequence in context: A131552 A122369 A005978 this_sequence A137636 A027618 A020060
Adjacent sequences: A083062 A083063 A083064 this_sequence A083066 A083067 A083068
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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 21 2003
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