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A015565
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a(n) = 7*a(n-1) + 8*a(n-2).
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20
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
General form: k=8^n-k. Also: A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n)=8^n/9-(-1)^n/9. a(n)=J(3*n)/3=A001045(3*n)/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
a(n)=Sum_{k, 0<=k<=n} A106566(n,k)*A099322(k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 30 2008]
a(n)=round(8^n/9). [From Mircea Merca, Dec 28 2010]
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MAPLE
| seq(round(8^n/9), n=0..25) [From Mircea Merca, Dec 28 2010]
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MATHEMATICA
| k=0; lst={k}; Do[k=8^n-k; AppendTo[lst, k], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
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PROG
| (Sage) [lucas_number1(n, 7, -8) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 24 2009]
(MAGMA) [Round(8^n/9): n in [0..30]]; // Vincenzo Librandi, Jun 24 2011
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CROSSREFS
| Cf. A082311, A082365.
Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
Sequence in context: A201872 A082310 A014990 * A082413 A142990 A202250
Adjacent sequences: A015562 A015563 A015564 * A015566 A015567 A015568
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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