Search: id:A001924
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%I A001924 M2645 N1053
%S A001924 0,1,3,7,14,26,46,79,133,221,364,596,972,1581,2567,4163,
%T A001924 6746,10926,17690,28635,46345,75001,121368,196392,317784,
%U A001924 514201,832011,1346239,2178278,3524546,5702854,9227431
%N A001924 Apply partial sum operator twice to Fibonacci numbers.
%C A001924 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
%C A001924 A107909(a(n)) = A000225(n) = 2^n - 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 28 2005
%C A001924 (1, 3, 7, 14,...) = row sums of triangle A141289. - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Jun 22 2008
%D A001924 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001924 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001924 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.
%D A001924 J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
%D A001924 W. Lang, Problem B-858, Fibonacci Quarterly, 36 (1998), 373-374, ibid. 
               37 (1999) 183-184.
%H A001924 T. D. Noe, <a href="b001924.txt">Table of n, a(n) for n=0..500</a>
%H A001924 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A001924 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A001924 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A001924 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) 
               ]
%F A001924 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
%F A001924 a(n)=sum(k=0, n, sum(i=0, k, F(i))). - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Jan 26 2003
%F A001924 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
%F A001924 a(n)=sum(k=0, n, F(k)*(n-k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Jun 07 2004
%F A001924 a(n) - a(n-1) = A101220(1,1,n). - Ross La Haye (rlahaye(AT)new.rr.com), 
               May 31 2006
%F A001924 F(n) + a(n-3) = A133640(n). - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Sep 19 2007
%F A001924 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
%p A001924 A001924:=-1/(z**2+z-1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 
               dissertation.]
%t A001924 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]
%Y A001924 Cf. A000045, A001891.
%Y A001924 Right-hand column 4 of triangle A011794.
%Y A001924 Cf. A133640.
%Y A001924 Cf. A141289.
%Y A001924 Sequence in context: A008646 A036830 A014153 this_sequence A079921 A014168 
               A132109
%Y A001924 Adjacent sequences: A001921 A001922 A001923 this_sequence A001925 A001926 
               A001927
%K A001924 nonn,easy,nice
%O A001924 0,3
%A A001924 N. J. A. Sloane (njas(AT)research.att.com).
%E A001924 Better description 1/97.

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