0,3

Leading coefficients in certain rook polynomials (for n>=2; see p. 18 of the Riordan paper). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 08 2004

A107909(a(n)) = A000225(n) = 2^n - 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 28 2005

(1, 3, 7, 14,...) = row sums of triangle A141289. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 22 2008

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (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.

J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.

W. Lang, Problem B-858, Fibonacci Quarterly, 36 (1998), 373-374, ibid. 37 (1999) 183-184.

T. D. Noe, Table of n, a(n) for n=0..500

Index entries for sequences related to linear recurrences with constant coefficients

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.

G.f.: x/((1-x-x^2)*(1-x)^2). Convolution of natural numbers n >= 1 with Fibonacci numbers F(k). a(n)=F(n+4)-(3+n) [ Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) ]

a(n) = a(n-1)+a(n-2)+n = Fib(n+4)-n-3 = a(n-1)+A000071(n+2) = A001891(n)-a(n-1) = n+A001891(n-1) = A065220(n+4)+1 = A000126(n+1)-1. - Henry Bottomley (se16(AT)btinternet.com), Jan 03 2003

a(n)=sum(k=0, n, sum(i=0, k, F(i))). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 26 2003

a(n)=(sqrt(5)/2+1/2)^n(7sqrt(5)/10+3/2)+(3/2-7sqrt(5)/10)(sqrt(5)/2-1/2)^n*(-1)^n-n-3 - Paul Barry (pbarry(AT)wit.ie), Mar 26 2003

a(n)=sum(k=0, n, F(k)*(n-k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 07 2004

a(n) - a(n-1) = A101220(1,1,n). - Ross La Haye (rlahaye(AT)new.rr.com), May 31 2006

F(n) + a(n-3) = A133640(n). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 19 2007

a(n)=Sum_{k=1..n}{C(n-k+2,k+1)}, with n>=0. - Paolo P. Lava (ppl(AT)spl.at), Apr 16 2008

A001924:=-1/(z**2+z-1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]

lst={}; s0=s1=0; Do[s0+=a[n]; s1+=s0; AppendTo[lst, s1], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 10 2008]

Cf. A000045, A001891.

Right-hand column 4 of triangle A011794.

Cf. A133640.

Cf. A141289.

Adjacent sequences: A001921 A001922 A001923 this_sequence A001925 A001926 A001927

Sequence in context: A008646 A036830 A014153 this_sequence A079921 A014168 A132109

nonn,easy,nice

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

Better description 1/97.