The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A328988 Number of partitions of n with rank a multiple of 3. 2
 1, 0, 1, 3, 1, 3, 7, 6, 10, 16, 16, 25, 37, 43, 58, 81, 95, 127, 168, 205, 264, 340, 413, 523, 660, 806, 1002, 1248, 1513, 1866, 2292, 2775, 3379, 4116, 4949, 5989, 7227, 8659, 10393, 12464, 14845, 17720, 21109, 25041, 29708, 35210, 41562, 49085, 57871, 68052 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 Elaine Hou and Meena Jagadeesan, Dyson’s partition ranks and their multiplicative extensions, arXiv:1607.03846 [math.NT], 2016; The Ramanujan Journal 45.3 (2018): 817-839. See Table 2. FORMULA a(n) = A000041(n) - 2*A328989(n). - Alois P. Heinz, Nov 11 2019 MAPLE b:= proc(n, i, r) option remember; `if`(n=0 or i=1,       `if`(irem(r+n, 3)=0, 1, 0), b(n, i-1, r)+         b(n-i, min(n-i, i), irem(r+1, 3)))     end: a:= proc(n) option remember; add(       b(n-i, min(n-i, i), modp(1-i, 3)), i=1..n)     end: seq(a(n), n=1..60);  # Alois P. Heinz, Nov 11 2019 MATHEMATICA b[n_, i_, r_] := b[n, i, r] = If[n == 0 || i == 1, If[Mod[r + n, 3] == 0, 1, 0], b[n, i - 1, r] + b[n - i, Min[n - i, i], Mod[r + 1, 3]]]; a[n_] := a[n] = Sum[b[n - i, Min[n - i, i], Mod[1 - i, 3]], {i, 1, n}]; Array[a, 60] (* Jean-François Alcover, Feb 29 2020, after Alois P. Heinz *) CROSSREFS Cf. A000041, A328989. Sequence in context: A092689 A281553 A064434 * A086401 A095732 A001644 Adjacent sequences:  A328985 A328986 A328987 * A328989 A328990 A328991 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 09 2019 EXTENSIONS a(33)-a(50) from Lars Blomberg, Nov 11 2019 Typo in a(14) in both the arXiv preprint and the published version in the Ramanujan Journal corrected by Alois P. Heinz, Nov 11 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 16 07:59 EDT 2021. Contains 343030 sequences. (Running on oeis4.)