1,2

a(n) = A125118(n,5) for n>4. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 21 2006

a(n)=6*a(n-1)+1 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 29 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

C. Banderier and D. Merlini, Lattice paths with an infinite set of jumps, FPSAC02, Melbourne, 2002.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 375

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Binomial transform of A003948. If preceded by 0, then binomial transform of powers of 5, A000351 (preceded by 0). - Paul Barry (pbarry(AT)wit.ie), Mar 28 2003

a(n)=Sum{k=1..n, C(n, k)5^(k-1) }. E.g.f.: (exp(6x) - exp(x))/5 (offset 0). - Paul Barry (pbarry(AT)wit.ie), Mar 28 2003

G.f.: 1/((1-1x)(1-6x)) - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 06 2005

a:=n->sum(6^(n-j), j=1..n): seq(a(n), n=1..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 04 2007

A003464:=1/(6*z-1)/(z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=5*a[n-1]+6*a[n-2]+2 od: seq(a[n], n=1..33); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 14 2008]

lst={}; Do[p=(6^n-1)/5; AppendTo[lst, p], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 29 2008]

(PARI) for(n=0, 10, print1(polcoeff(1/((1-1*x)*(1-6*x)), n), ", ")) for(n=1, 10, print1((6^n-1)/5, ", "))

(Other) sage: [lucas_number1(n, 7, 6) for n in xrange(1, 22)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]

(Other) sage: [gaussian_binomial(n, 1, 6) for n in xrange(1, 22)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]

Sequence in context: A043553 A049609 A161728 this_sequence A022036 A015451 A126502

Adjacent sequences: A003461 A003462 A003463 this_sequence A003465 A003466 A003467

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 21 2006