A288120 Number of partitions of n into distinct pentanacci numbers (with a single type of 1) (A001591).

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

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: A078315 A365685 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