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A000784 Symmetrical planar partitions of n: planar partitions (A000219) that when regarded as 3-D objects have just one symmetry plane).
(Formerly M0322 N0119)
9
0, 1, 2, 2, 4, 6, 6, 11, 16, 20, 28, 41, 51, 70, 93, 122, 158, 211, 266, 350, 450, 577, 730, 948, 1186, 1510, 1901, 2408, 2999, 3790, 4703, 5898, 7310, 9111, 11231, 13979, 17168, 21229, 26036, 32095, 39188, 48155, 58657, 71798, 87262, 106472, 129014 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

P. A. MacMahon, Combinatory Analysis. Cambridge Univ. Press, London and New York, Vol. 1, 1915 and Vol. 2, 1916; see vol. 2, p 332.

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).

LINKS

Jean-François Alcover, Table of n, a(n) for n = 1..150

P. A. MacMahon, Combinatory analysis.

MATHEMATICA

nmax = 150;

a219[0] = 1;

a219[n_] := a219[n] = Sum[a219[n - j] DivisorSigma[2, j], {j, n}]/n;

s = Product[1/(1 - x^(2 i - 1))/(1 - x^(2 i))^Floor[i/2], {i, 1, Ceiling[( nmax + 1)/2]}] + O[x]^( nmax + 1);

A005987 = CoefficientList[s, x];

a048140[n_] := (a219[n] + A005987[[n + 1]])/2;

A048141 = Cases[Import["https://oeis.org/A048141/b048141.txt", "Table"], {_, _}][[All, 2]];

a[1] = 0;

a[n_] := -A048141[[n]] + 2 a048140[n] - a219[n];

a /@ Range[1, nmax] (* Jean-François Alcover, Dec 28 2019 *)

CROSSREFS

Equals -A048141 + 2*A048140 - A000219. Cf. A000785, A000786, A005987, A048142.

Sequence in context: A055388 A065457 A280366 * A092991 A102425 A162608

Adjacent sequences:  A000781 A000782 A000783 * A000785 A000786 A000787

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wouter Meeussen

STATUS

approved

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Last modified May 8 20:32 EDT 2021. Contains 343668 sequences. (Running on oeis4.)