0,4

Also n-stacks with strictly receding left wall.

F. C. Auluck, On some new types of partitions associated with generalized Ferrers graphs. Proc. Cambridge Philos. Soc. 47, (1951), 679-686.

R. K. Guy, The second strong law of small numbers. Math. Mag. 63 (1990), no. 1, 3-20.

E. M. Wright, Stacks, III, Quart. J. Math. Oxford, 23 (1972), 153-158.

T. D. Noe, Table of n, a(n) for n = 0..1000

Erich Friedman, Illustration of initial terms

D. Gouyou-Beauchamps and P. Leroux, Enumeration of symmetry classes of convex polyominoes on the honeycomb lattice.

For a(6)=8 we have the following stacks:

..x

.xx .xx. ..xx .x... ..x.. ...x. ....x

xxx xxxx xxxx xxxxx xxxxx xxxxx xxxxx xxxxxx

Comment from Franklin T. Adams-Watters, Jan 18 2007: For a(7) = 12 we have the following stacks:

..x. ...x

.xx. ..xx .xxx .xx.. ..xx. ...xx

xxxx xxxx xxxx xxxxx xxxxx xxxxx

and

.x.... ..x... ...x.. ....x. .....x

xxxxxx xxxxxx xxxxxx xxxxxx xxxxxx xxxxxxx

s := 1+sum(z^(n*(n+1)/2)/((1-z^(n))*product((1-z^i), i=1..n-1)^2), n=1..50): s2 := series(s, z, 300): for j from 1 to 100 do printf(`%d, `, coeff(s2, z, j)) od:

(PARI) a(n)=if(n<0, 0, polcoeff(sum(k=0, (sqrt(8*n+1)-1)/2, x^((k^2+k)/2)/prod(i=1, k, (1-x^i+x*O(x^n))^((i<k)+1))), n))

Cf. A001522, A001523.

Adjacent sequences: A001521 A001522 A001523 this_sequence A001525 A001526 A001527

Sequence in context: A084376 A098693 A122928 this_sequence A136275 A078408 A007478

nonn,nice,easy

njas

Maple code and more terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 27 2001