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A288120 Number of partitions of n into distinct pentanacci numbers (with a single type of 1) (A001591). 3
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,32

COMMENTS

The first occurrences of 1, 2, 3, 4, 5, ... are at n=0, 31, 912, 1824, 26815, ... - Antti Karttunen, Dec 22 2017

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..52656

Eric Weisstein's World of Mathematics, Fibonacci n-Step Number

Eric Weisstein's World of Mathematics, Pentanacci Number

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=5} (1 + x^A001591(k)).

EXAMPLE

a(31) = 2 because we have [31] and [16, 8, 4, 2, 1].

PROG

(PARI)

A001591(n) = { if(n<=3, return(0)); my(p0=0, p1=0, p2=0, p3=1, p4=1, old_p0); while(n>5, n--; old_p0=p0; p0=p1; p1=p2; p2=p3; p3=p4; p4=old_p0+p0+p1+p2+p3; ); p4; }

v288120nthgen(up_to) = { my(k=6, fk, vec = [1], vec2); while(k<=up_to, fk = A001591(k); k++; vec2 = vector(length(vec)+fk, i, (i==fk)+if(i>fk, vec[i-fk], 0)+if(i<=length(vec), vec[i], 0)); vec = vec2); vector(fk, i, vec[i]); }

write_to_bfile_with_a0_as_given(a0, vec, bfilename) = { write(bfilename, 0, " ", a0); for(n=1, length(vec), write(bfilename, n, " ", vec[n])); }

write_to_bfile_with_a0_as_given(1, v288120nthgen(21), "b288120.txt"); \\ Antti Karttunen, Dec 22 2017

(Scheme)

(define (A288120 n) (let ((s (list 0))) (let fork ((r n) (i 5)) (cond ((zero? r) (set-car! s (+ 1 (car s)))) ((> (A001591 i) r) #f) (else (begin (fork (- r (A001591 i)) (+ 1 i)) (fork r (+ 1 i)))))) (car s)))

;; This one uses memoization-macro definec

(definec (A001591 n) (cond ((<= n 3) 0) ((= 4 n) 1) (else (+ (A001591 (- n 1)) (A001591 (- n 2)) (A001591 (- n 3)) (A001591 (- n 4)) (A001591 (- n 5))))))

;; Antti Karttunen, Dec 22 2017

CROSSREFS

Cf. A001591, A000119, A000121, A003263, A117546, A287656, A296209.

Sequence in context: A272901 A078315 A346418 * A156264 A249770 A298481

Adjacent sequences:  A288117 A288118 A288119 * A288121 A288122 A288123

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jun 05 2017

EXTENSIONS

More terms from Antti Karttunen, Dec 22 2017

STATUS

approved

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Last modified July 25 21:44 EDT 2021. Contains 346294 sequences. (Running on oeis4.)