0,2

a(n-2)=(((-I)^(n-2))/2)*diff(S(n,x),x$2)|_{x=I}, n>=2. Second derivative of Chebyshev S-polynomials evaluated at x=I (imaginary unit) multiplied by ((-I)^(n-2))/2. See A049310 for the S-polynomials. W. Lang, Apr 04 2007.

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.

V. E. Hoggatt, Jr. and M. Bicknell-Johnson, Fibonacci convolution sequences, Fib. Quart., 15 (1977), 117-122.

J. Riordan, Combinatorial Identities, Wiley, 1968, p. 101.

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

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.

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

T. Mansour, Generalization of some identities involving the Fibonacci numbers

P. Moree, Convoluted convolved Fibonacci numbers

Pieter Moree, Convoluted Convolved Fibonacci Numbers, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.2.

G.f.: ( 1 - x - x^2 )^-3.

a(n)= ((5*n+16)*(n+1)*F(n+2)+(5*n+17)*(n+2)*F(n+1))/50, F(n)=A000045(n). - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 12 2000

For n>2, a(n-2)= sum(i+j+k=n, F(i)*F(j)*F(k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 01 2002

a(n)=F''(n+2, 1)/2, i.e., 1/2 times the 2nd derivative of the (n+2)th Fibonacci polynomial evaluated at 1. - T. D. Noe (noe(AT)sspectra.com), Jan 18 2006

a(n)=sum{k=0..n, C(k,n-k)*C(k+2,2)}; - Paul Barry (pbarry(AT)wit.ie), Apr 13 2008

A001628:=-1/(z**2+z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]

a(n)= A037027(n+2, 2) (Fibonacci convolution triangle).

Cf. A055243.

Adjacent sequences: A001625 A001626 A001627 this_sequence A001629 A001630 A001631

Sequence in context: A000711 A121589 A000716 this_sequence A099166 A054442 A114697

easy,nonn,new

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