

A100853


Number of partitions of n in which every part occurs 1, 4, or 5 times. Also number of partitions of n in which every part is congruent to {1, 3, 4, 5, 7} mod 8.


2



1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 15, 19, 25, 31, 38, 48, 59, 72, 88, 107, 130, 157, 188, 225, 270, 321, 380, 451, 533, 627, 737, 864, 1011, 1181, 1375, 1599, 1858, 2152, 2488, 2875, 3316, 3816, 4387, 5036, 5773, 6610, 7555, 8626, 9840, 11207, 12748, 14489
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OFFSET

0,4


COMMENTS

Also number of partitions of n in which every even part occurs exactly twice.  Vladeta Jovovic, Oct 06 2007


LINKS

Table of n, a(n) for n=0..51.


FORMULA

Euler transform of period 8 sequence [1, 0, 1, 1, 1, 0, 1, 0, ...]. G.f.: Product_{k>0} (1+x^k)*(1+x^(4*k)) = 1/Product_{k>0} (1x^A047501(k)).
a(n) ~ 5^(1/4) * exp(sqrt(5*n/3)*Pi/2) / (8 * 3^(1/4) * n^(3/4)).  Vaclav Kotesovec, Aug 14 2018


MAPLE

seq(coeff(mul((1+x^k)*(1+x^(4*k)), k=1..100), x, n), n=0..60); (C. Ronaldo)


MATHEMATICA

np145Q[j_]:=SubsetQ[{1, 4, 5}, Union[Tally[j][[All, 2]]]]; Table[Length[ Select[ IntegerPartitions[n], np145Q]], {n, 0, 51}] (* Harvey P. Dale, Aug 04 2018 *)


CROSSREFS

Cf. A089958.
Sequence in context: A122129 A280909 A003413 * A174065 A121659 A096814
Adjacent sequences: A100850 A100851 A100852 * A100854 A100855 A100856


KEYWORD

easy,nonn


AUTHOR

Vladeta Jovovic, Jan 08 2005


EXTENSIONS

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 19 2005


STATUS

approved



