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Search: id:A001524
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| A001524 |
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Number of stacks, or arrangements of n pennies in contiguous rows, each touching 2 in row below.
(Formerly M0687 N0253)
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+0
4
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| 1, 1, 1, 2, 3, 5, 8, 12, 18, 26, 38, 53, 75, 103, 142, 192, 260, 346, 461, 607, 797, 1038, 1348, 1738, 2234, 2856, 3638, 4614, 5832, 7342, 9214, 11525, 14369, 17863, 22142, 27371, 33744, 41498, 50903, 62299, 76066, 92676, 112666, 136696, 165507, 200018
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Also n-stacks with strictly receding left wall.
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REFERENCES
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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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
E. M. Wright, Stacks, III, Quart. J. Math. Oxford, 23 (1972), 153-158.
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LINKS
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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.
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EXAMPLE
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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
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MAPLE
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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:
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PROGRAM
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(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))
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CROSSREFS
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Cf. A001522, A001523.
Sequence in context: A084376 A098693 A122928 this_sequence A136275 A078408 A007478
Adjacent sequences: A001521 A001522 A001523 this_sequence A001525 A001526 A001527
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Maple code and more terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 27 2001
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