0,2

a(n)= ((n+1)*F(2*n+3)+(2*n+3)*F(2*(n+1)))/5 with F(n)=A000045(n) (Fibonacci numbers). One half of odd indexed A001629(n), n >= 2, (Fibonacci convolution).

Convolution of F(2n+1) (A001519) and F(2n+2) (A001906(n+1)) - Graeme McRae (g_m(AT)mcraefamily.com), Jun 07 2006

Number of reentrant corners along the lower contours of all directed column-convex polyominoes of area n+3 (a reentrant corner along the lower contour is a vertical step that is followed by a horizontal step). a(n)=Sum(k*A121466(n+3,k), k=0..ceil((n+1)/2)). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 02 2006

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.

E. Barcucci, R. Pinzani and R. Sprugnoli, Directed column-convex polyominoes by recurrence relations, Lecture Notes in Computer Science, No. 668, Springer, Berlin (1993), pp. 282-298.

E. Deutsch and H. Prodinger, A bijection between directed column-convex polyominoes and ordered trees of height at most three, Theoretical Comp. Science, 307, 2003, 319-325.

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.

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

a(n)=sum(k*binom(n+k+1, 2k), k=1..n+1) - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 11 2003

A001870:=-(-1+z)/(z**2-3*z+1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]

a(n)= A060921(n+1, 1)/2.

Partial sums of A030267. First differences of A001871.

Cf. A121466.

Sequence in context: A003296 A053545 A049612 this_sequence A025568 A001047 A099448

Adjacent sequences: A001867 A001868 A001869 this_sequence A001871 A001872 A001873

nonn

njas

More terms from Christian G. Bower (bowerc(AT)usa.net).