1,2

The inverse binomial transform is 1,1,3,6,..., i.e. the unsigned version of A077926. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 15 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).

I. G. Enting and A. J. Guttmann, On the area of square lattice polygons, J. Statist. Phys., 58 (1990), 475-484.

Dean Hickerson, Counting Horizontally Convex Polyominoes, J. Integer Sequences, Vol. 2 (1999), #99.1.8.

D. A. Klarner, The number of graded partially ordered sets, J. Combin. Theory, 6 (1969), 12-19.

W. F. Lunnon, Counting polyominoes, pp. 347-372 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.

R. P. Stanley, Enumerative Combinatorics I, p. 259.

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.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

D. Zeilberger, [math/9801016] Automated counting of LEGO towers

Hickerson reference.

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 367

G.f.: x*(1-x)^3/(1-5*x+7*x^2-4*x^3). a(n) = 5a(n-1) - 7a(n-2) + 4a(n-3) for n >= 5.

A001169:=(z-1)**3/(-1+5*z-7*z**2+4*z**3); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]

a[ n_ ] := a[ n ]=If[ n<5, {1, 2, 6, 19}[ [ n ] ], 5a[ n-1 ]-7a[ n-2 ]+4a[ n-3 ] ].

a(n) = a(n-1) + A049219(n) + A049220(n) for n >= 2.

Cf. A049219-A049222.

Sequence in context: A014346 A118364 A052544 this_sequence A022041 A018906 A014010

Adjacent sequences: A001166 A001167 A001168 this_sequence A001170 A001171 A001172

nonn,nice,easy

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

More terms from Dean Hickerson (dean.hickerson(AT)yahoo.com)