0,2

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.

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 260.

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.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 389

G.f.: 1/((1-3*x)*(1-x)^2). a(n)=(3^(n+2)-2*n-5)/4.

a(n)=sum{k=0..n+1, (n-k+1)3^k}=sum{k=0..n+1, k*3^(n-k+1)} - Paul Barry (pbarry(AT)wit.ie), Jul 30 2004

a(n)=sum{k=0..n, binomial(n+2, k+2)2^k} - Paul Barry (pbarry(AT)wit.ie), Jul 30 2004

a(-1)=0, a(0)=1, a(n)=4*a(n-1)-3*a(n-2)+1 - Miklos Kristof (kristmikl(AT)freemail.hu), Mar 09 2005

a(n) = right term of M^(n+1) * [1,0,0]; where M = the 3 X 3 matrix [1,0,0; 1,1,0; 1,1,3]. E.g. a(4) = 179 since M^5 = [1, 5, 179]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 28 2006

a[ -1]:=0:a[0]:=1:for n from 1 to 50 do a[n]:=4*a[n-1]-3*a[n-2]+1 od: seq(a[n], n=0..50); (Kristof)

A000340:=-1/(3*z-1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]

a:=n->sum(3^(n-j)*j, j=0..n): seq(a(n), n=1..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2008

Sequence in context: A093374 A000745 A128553 this_sequence A034567 A133648 A099449

Adjacent sequences: A000337 A000338 A000339 this_sequence A000341 A000342 A000343

nonn,easy

njas, Simon Plouffe (plouffe(AT)math.uqam.ca)