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A331330 a(n) is the number of sparse rulers of length n where the length of the first segment is unique. 2
0, 1, 1, 3, 4, 8, 14, 26, 46, 85, 155, 286, 528, 980, 1824, 3410, 6392, 12022, 22675, 42885, 81312, 154540, 294362, 561849, 1074463, 2058462, 3950220, 7592403, 14614105, 28168227, 54363000, 105043517, 203200635, 393496975, 762765642, 1479957400, 2874038529, 5585986973, 10865544853, 21150913457, 41201771886 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A sparse ruler, or simply a ruler, is a strict increasing finite sequence of nonnegative integers starting from 0 called marks. See A103294 for more definitions.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2000 (first 101 terms from Bert Dobbelaere)

FORMULA

a(n) = A331332(n,1) for n >= 1.

EXAMPLE

All rulers of length four are listed below; those marked with x are counted: [0,4]x, [0,3,4]x, [0,2,4], [0,1,4]x, [0,2,3,4]x, [0,1,3,4], [0,1,2,4], [0,1,2,3,4].

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, add(

     `if`(i=j, 0, b(n-j, `if`(n<i+j, 0, i))), j=1..n))

    end:

a:= proc(n) option remember; add(b(n-j, j), j=1..n) end:

seq(a(n), n=0..50);  # Alois P. Heinz, Feb 06 2020

PROG

(Python)

cache={}

def f( n, l1):

..args=(n, l1)

..if args in cache: return cache[args]

..s=0

..for l in range(1, n+1):

....if l!=l1:

......s += 1 if l==n else f(n-l, l1)

..cache[args] = s

..return s

def a331330(n):

..if n==0: return 0

..s=1

..for l1 in range(1, n+1):

....s += f( n-l1, l1)

..return s

# Bert Dobbelaere, Feb 06 2020

CROSSREFS

Cf. A331332, A103294.

Sequence in context: A170902 A000205 A136425 * A005907 A049866 A118355

Adjacent sequences:  A331327 A331328 A331329 * A331331 A331332 A331333

KEYWORD

nonn

AUTHOR

Peter Luschny, Jan 24 2020

EXTENSIONS

More terms from Bert Dobbelaere, Feb 06 2020

STATUS

approved

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Last modified May 27 12:27 EDT 2020. Contains 334657 sequences. (Running on oeis4.)