0,3

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]

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

a(n)=Sum_{k, 0<=k<=n} A106566(n,k)*A099322(k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 30 2008]

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]

(Other) sage: [lucas_number1(n, 7, -8) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 24 2009]

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: A042187 A082310 A014990 this_sequence A082413 A142990 A147689

Adjacent sequences: A015562 A015563 A015564 this_sequence A015566 A015567 A015568

nonn,easy

Olivier Gerard (olivier.gerard(AT)gmail.com)