A100853 - OEIS

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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.

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

(list; graph; refs; listen; history; text; internal format)

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} (1-x^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