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Search: id:A084640
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| A084640 |
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Generalized Jacobsthal numbers. |
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+0
2
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| 0, 1, 5, 11, 25, 51, 105, 211, 425, 851, 1705, 3411, 6825, 13651, 27305, 54611, 109225, 218451, 436905, 873811, 1747625, 3495251, 6990505, 13981011, 27962025, 55924051, 111848105, 223696211, 447392425, 894784851, 1789569705, 3579139411
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n)=A001045(n+2)+4*A000975(n-3).
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FORMULA
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G.f.: x(1+3x)/((1+x)(1-x)(1-2x)); a(n)=a(n-1)+2a(n-2)+4, a(0)=0, a(1)=1; a(n)=5*2^n/3+(-1)^n/3-2.
a(n)=5a(n-2)-4a(n-4). Same recurrence as in A083639, A101622. - Paul Curtz (bpcrtz(AT)free.fr), Apr 03 2008
a(n+1)-2a(n) = period 2: repeat 1, 3. - Paul Curtz (bpcrtz(AT)free.fr), Apr 03 2008
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CROSSREFS
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Cf. A000975, A000225, A084639.
Adjacent sequences: A084637 A084638 A084639 this_sequence A084641 A084642 A084643
Sequence in context: A122925 A021008 A059358 this_sequence A056739 A003598 A014858
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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 06 2003
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