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

Author

Ilya Gutkovskiy, Jun 05 2017

Keywords

• nonn

Comments

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

Examples

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

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

Crossrefs

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

Programs

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

Formula

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

Extensions

More terms from Antti Karttunen, Dec 22 2017