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
Keywords
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
Programs
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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
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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
Comments