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A331981 Number of compositions (ordered partitions) of n into distinct odd primes. 3
1, 0, 0, 1, 0, 1, 0, 1, 2, 0, 2, 1, 2, 1, 2, 6, 4, 1, 4, 7, 4, 12, 4, 13, 6, 12, 28, 18, 28, 19, 6, 25, 52, 24, 54, 30, 56, 31, 98, 156, 102, 37, 104, 157, 150, 276, 150, 175, 154, 288, 200, 528, 246, 307, 226, 666, 990, 780, 1038, 679, 348, 799, 1828, 1272, 1162, 1164 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

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

Index entries for sequences related to compositions

EXAMPLE

a(16) = 4 because we have [13, 3], [11, 5], [5, 11] and [3, 13].

MAPLE

s:= proc(n) option remember; `if`(n<1, 0, ithprime(n+1)+s(n-1)) end:

b:= proc(n, i, t) option remember; `if`(s(i)<n, 0, `if`(n=0, t!, (p

      ->`if`(p>n, 0, b(n-p, i-1, t+1)))(ithprime(i+1))+b(n, i-1, t)))

    end:

a:= n-> b(n, numtheory[pi](n), 0):

seq(a(n), n=0..72);  # Alois P. Heinz, Feb 03 2020

MATHEMATICA

s[n_] := s[n] = If[n < 1, 0, Prime[n + 1] + s[n - 1]];

b[n_, i_, t_] := b[n, i, t] = If[s[i] < n, 0, If[n == 0, t!, If[# > n, 0, b[n - #, i - 1, t + 1]]&[Prime[i + 1]] + b[n, i - 1, t]]];

a[n_] := b[n, PrimePi[n], 0];

a /@ Range[0, 72] (* Jean-Fran├žois Alcover, Nov 09 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A002124, A023360, A024939, A065091, A099773, A219107, A331926, A331982.

Sequence in context: A192541 A281545 A332033 * A099302 A219198 A025814

Adjacent sequences:  A331978 A331979 A331980 * A331982 A331983 A331984

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 03 2020

STATUS

approved

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Last modified January 28 06:43 EST 2022. Contains 350654 sequences. (Running on oeis4.)