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Search: id:A015565
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| A015565 |
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a(n) = 7 a(n-1) + 8 a(n-2). |
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+0
9
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| 0, 1, 7, 57, 455, 3641, 29127, 233017, 1864135, 14913081, 119304647, 954437177, 7635497415, 61083979321, 488671834567, 3909374676537, 31274997412295, 250199979298361, 2001599834386887, 16012798675095097, 128102389400760775
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A linear 2nd order recurrence. A Jacobsthal number sequence.
Second binomial transform of A080424. Binomial transform of A053573, with leading zero. Binomial transform is 0,1,9,81,729,....(9^n/9-0^n/9). Second binomial transform is 0,1,11,111,1111,... (A002275: repunits). - Paul Barry (pbarry(AT)wit.ie), Mar 14 2004
Number of walks of length n between any two distinct nodes of the complete graph K_9. Example: a(2)=7 because the walks of length 2 between the nodes A and B of the complete graph ABCDEFGHI are: ACB, ADB, AEB, AFB, AGB, AHB, and AIB. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
Unsigned version of A014990 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 13 2007
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FORMULA
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a(n)=8^n/9-(-1)^n/9. a(n)=J(3n)/3=A001045(3n)/3. Binomial transform of A053573 (preceded by zero). - Paul Barry (pbarry(AT)wit.ie), Apr 09 2003
a(n)=8^(n-1)-a(n-1). G.f.=x/(1-7x-8x^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
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CROSSREFS
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Cf. A082311, A082365.
Sequence in context: A042187 A082310 A014990 this_sequence A082413 A062192 A122649
Adjacent sequences: A015562 A015563 A015564 this_sequence A015566 A015567 A015568
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (ogerard(AT)ext.jussieu.fr)
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