

A144559


a(n) = number of triples [i,j,k] with i+j+k = n, i an odd prime, j an odd Fibonacci number and k a positive Fibonacci number.


1



0, 0, 0, 0, 1, 1, 3, 2, 6, 3, 7, 3, 7, 4, 6, 5, 8, 5, 10, 5, 12, 5, 10, 5, 12, 7, 13, 6, 15, 4, 12, 6, 13, 7, 13, 5, 16, 5, 13, 8, 11, 8, 11, 7, 17, 8, 15, 6, 12, 8, 11, 10, 13, 7, 13, 6, 12, 9, 12, 8, 14, 7, 19, 8, 18, 10, 16, 9, 15, 9, 16, 6, 16, 9, 19, 11, 18, 7, 19, 8, 16, 10, 14, 7, 18, 8, 21
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OFFSET

1,7


COMMENTS

ZhiWei SUN conjectured on the Number Theory Mailing List that a(n) > 0 for all n > 4.
The conjecture has been verified by D. S. McNeil for all n < 10^13.


LINKS

Table of n, a(n) for n=1..87.


EXAMPLE

5 = 3+1+1, 6 = 3+1+2, 7 = 5+1+1 = 3+3+1 = 3+1+3.


MAPLE

with(combinat); F:=fibonacci; ans:=array(1..100); oF:=[]; pF:=[];
for n from 1 to 100 do ans[n] := 0; od:
for n from 2 to 12 do if F(n) mod 2 = 1 then oF:=[op(oF), F(n)]; fi; od;
for n from 2 to 12 do pF:=[op(pF), F(n)]; od:
for i from 2 to 30 do t1:=ithprime(i);
for j from 1 to nops(oF) do t2:=t1+oF[j]:
for k from 1 to nops(pF) do t3:=t2+pF[k];
if t3 <= 100 then ans[t3]:=ans[t3]+1; fi;
od: od: od: [seq(ans[n], n=1..100)];


CROSSREFS

See A154257 for a better version.
Sequence in context: A257698 A322907 A071018 * A155114 A038572 A245676
Adjacent sequences: A144556 A144557 A144558 * A144560 A144561 A144562


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Jan 03 2009


STATUS

approved



