The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A323583 Number of ways to split an integer partition of n into consecutive subsequences. 26
 1, 1, 3, 7, 17, 37, 83, 175, 373, 773, 1603, 3275, 6693, 13557, 27447, 55315, 111397, 223769, 449287, 900795, 1805465, 3615929, 7240327, 14491623, 29001625, 58027017, 116093259, 232237583, 464558201, 929224589, 1858623819, 3717475031, 7435314013, 14871103069 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) = A070933(n)/2. O.g.f.: (1/2)*Product_{n >= 1} 1/(1 - 2*x^n). G.f.: 1 + Sum_{k>=1} 2^(k - 1) * x^k / Product_{j=1..k} (1 - x^j). - Ilya Gutkovskiy, Jan 28 2020 EXAMPLE The a(3) = 7 ways to split an integer partition of 3 into consecutive subsequences are (3), (21), (2)(1), (111), (11)(1), (1)(11), (1)(1)(1). MAPLE b:= proc(n, i) option remember; `if`(n=0, 1/2, `if`(i<1, 0, b(n, i-1) +`if`(i>n, 0, 2*b(n-i, i)))) end: a:= n-> ceil(b(n\$2)): seq(a(n), n=0..33); # Alois P. Heinz, Jan 01 2023 MATHEMATICA Table[Sum[2^(Length[ptn]-1), {ptn, IntegerPartitions[n]}], {n, 40}] (* Second program: *) (1/2) CoefficientList[1 - 1/QPochhammer[2, x] + O[x]^100 , x] (* Jean-François Alcover, Jan 02 2022, after Vladimir Reshetnikov in A070933 *) CROSSREFS Cf. A006951, A070933, A100883, A279784, A279786, A323433, A323582. Sequence in context: A111210 A033489 A357212 * A336724 A178941 A178155 Adjacent sequences: A323580 A323581 A323582 * A323584 A323585 A323586 KEYWORD nonn AUTHOR Gus Wiseman, Jan 19 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 31 01:17 EST 2023. Contains 359947 sequences. (Running on oeis4.)