OFFSET
0,4
REFERENCES
S. Viswanath (student, Dept. Math, Indian Inst. Technology, Kanpur) A Note on Partition Eigensequences, preprint, Nov 15 1996.
LINKS
Robert Israel, Table of n, a(n) for n = 0..1000
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
KEYWORD
nonn,eigen
AUTHOR
STATUS
approved