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A050366 Number of ways to write n as an lterm, where an lterm is an unordered sum which is either 2, or 1 + an ordered product of lterms. 3
1, 1, 1, 2, 2, 4, 4, 7, 8, 12, 12, 21, 21, 29, 33, 46, 46, 67, 67, 93, 101, 125, 125, 177, 181, 223, 238, 300, 300, 394, 394, 488, 512, 604, 620, 796, 796, 930, 972, 1182, 1182, 1450, 1450, 1712, 1804, 2054, 2054, 2510, 2526, 2924, 3016, 3483, 3483 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,4

LINKS

Michael De Vlieger, Table of n, a(n) for n = 2..10000

FORMULA

Shifts left under transform T where Ta has Dirichlet g.f.: 1/(1-A(s)).

EXAMPLE

The different ways of writing the numbers 2 through 7 as lterms are:

  2 = 2,

  3 = 1 + 2,

  4 = 1 + (1+2),

  5 = 1 + (1+1+2) = 1 + 2*2,

  6 = 1 + (1+1+1+2) = 1 + (1+2*2),

  7 = 1 + (1+1+1+1+2) = 1 + (1+1+2*2) = 1 + 2*(1+2) = 1 + (1+2)*2.

MATHEMATICA

Fold[Function[{a, n}, Append[a, DivisorSum[n, a[[#]] a[[n/# - 1]] &, # < n &]]], {1}, Range[2, 53]] (* Michael De Vlieger, Mar 14 2018 *)

PROG

(PARI) a(n)=if(n<2, 1, sumdiv(n, d, if(d<n, a(d)*a(n/d-1), 0))) \\ Benoit Cloitre, Mar 13 2018

CROSSREFS

Cf. A002033, A050318, A050319, A050365.

Sequence in context: A035944 A227134 A240013 * A027591 A027596 A007213

Adjacent sequences:  A050363 A050364 A050365 * A050367 A050368 A050369

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower, Oct 15 1999

STATUS

approved

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Last modified September 19 12:57 EDT 2019. Contains 327198 sequences. (Running on oeis4.)