A331165 - OEIS

A331165

a(n) = a(n-1) + p(n) if p(n) > a(n-1), otherwise a(n) = a(n-1) - p(n), where p is the partition function A000041 (assuming a(n) = 0 for n < 0).

1, 0, 2, 5, 0, 7, 18, 3, 25, 55, 13, 69, 146, 45, 180, 4, 235, 532, 147, 637, 10, 802, 1804, 549, 2124, 166, 2602, 5612, 1894, 6459, 855, 7697, 16046, 5903, 18213, 3330, 21307, 42944, 16929, 48114, 10776, 55359, 2185, 65446, 140621, 51487, 157045, 32291, 179564

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OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

MAPLE

a:= proc(n) option remember; `if`(n<0, 0, ((s, t)-> s+

`if`(s<t, t, -t))(a(n-1), combinat[numbpart](n)))

end:

seq(a(n), n=0..70);

MATHEMATICA

a[n_] := a[n] = If[n<0, 0, With[{a1 = a[n-1], p = PartitionsP[n]}, If[p>a1, a1 + p, a1 - p]]];

a /@ Range[0, 70] (* Jean-François Alcover, Jan 05 2021 *)

PROG

(PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, my(p = numbpart(n-1)); va[n] = va[n-1] - p; if (va[n] < 0, va[n] += 2*p); ); va; } \\ Michel Marcus, Jan 06 2021

CROSSREFS

Cf. A000041, A008344, A008345, A008348, A076042, A111466, A126646, A327442, A330725.

Sequence in context: A066033 A096319 A146105 * A022832 A008348 A201576

Adjacent sequences: A331162 A331163 A331164 * A331166 A331167 A331168

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 11 2020

STATUS

approved