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A027583
Sequence satisfies T(a)=a, where T is defined below.
1
1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 11, 13, 16, 18, 21, 23, 27, 31, 36, 39, 45, 50, 56, 63, 71, 78, 87, 97, 108, 120, 132, 144, 161, 177, 194, 213, 235, 255, 281, 307, 335, 365, 397, 431, 472, 512, 553, 600, 652, 704, 763, 823, 889, 959, 1035, 1112, 1201
OFFSET
0,4
REFERENCES
S. Viswanath (student, Dept. Math, Indian Inst. Technology, Kanpur) A Note on Partition Eigensequences, preprint, Nov 15 1996.
LINKS
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
FORMULA
Define T:a->b by: given a1<=a2<=..., remove duplicates, keep only numbers == +-1 mod 5, getting c1<c2<...; define b1, b2, ... by 1+Sum bi*x^i = Product 1/(1-x^ci).
MAPLE
A:= [1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 11, 13, 16]:
for nn from 17 to 101 do
C:= select(t -> t mod 5 = 1 or t mod 5 = 4, ListTools:-MakeUnique(A));
A:= [seq(coeff(series(mul(1/(1-x^c), c=C), x, nn), x, j), j=1..nn-1)];
od:
A; # Robert Israel, Nov 27 2016
MATHEMATICA
A = {1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 11, 13, 16};
For[nn = 17, nn <= 101, nn++, cc = Select[A // DeleteDuplicates, Mod[#, 5] == 1 || Mod[#, 5] == 4&]; A = Table[SeriesCoefficient[Product[1/(1- x^c), {c, cc}], {x, 0, j}], {j, 1, nn-1}];
];
A (* Jean-François Alcover, Sep 19 2018, from Robert Israel's Maple code *)
CROSSREFS
Sequence in context: A364915 A145816 A347610 * A029022 A140953 A112021
KEYWORD
nonn,eigen
STATUS
approved