|
|
A256171
|
|
Number of ways to write n as the sum of three unordered generalized heptagonal numbers.
|
|
2
|
|
|
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 1, 2, 1, 2, 3, 0, 1, 3, 1, 2, 3, 1, 1, 1, 1, 3, 3, 1, 2, 1, 2, 3, 1, 2, 4, 2, 1, 3, 2, 2, 3, 2, 1, 2, 2, 2, 3, 3, 2, 1, 2, 2, 3, 5, 2, 2, 2, 2, 3, 4, 2, 2, 4, 1, 3, 2, 1, 4, 3, 2, 2, 5, 2, 4, 3, 0, 4, 2, 1, 3, 6, 3, 3, 3, 1, 5, 2, 3, 5, 2, 2, 3, 3, 1, 5, 3, 1, 3, 3, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,9
|
|
COMMENTS
|
Conjecture: (i) a(n) > 0 except for n = 10, 16, 76, 307.
(ii) For any integer m > 2 not divisible by 4, each sufficiently large integer n can be written as the sum of three generalized m-gonal numbers.
In 1994 R. K. Guy noted that none of 10, 16 and 76 can be written as the sum of three generalized heptagonal numbers.
|
|
LINKS
|
|
|
EXAMPLE
|
a(157) = 1 since 157 = 3*(5*3-3)/2 + (-3)*(5*(-3)-3)/2 + 7*(5*7-3)/2.
a(748) = 1 since 748 = 0*(5*0-3)/2 + 0*(5*0-3)/2 + (-17)*(5*(-17)-3)/2.
|
|
MATHEMATICA
|
T[n_]:=Union[Table[x(5x-3)/2, {x, -Floor[(Sqrt[40n+9]-3)/10], Floor[(Sqrt[40n+9]+3)/10]}]]
L[n_]:=Length[T[n]]
Do[r=0; Do[If[Part[T[n], x]>n/3, Goto[aa]]; Do[If[Part[T[n], x]+2*Part[T[n], y]>n, Goto[bb]];
If[MemberQ[T[n], n-Part[T[n], x]-Part[T[n], y]]==True, r=r+1];
Continue, {y, x, L[n]}]; Label[bb]; Continue, {x, 1, L[n]}]; Label[aa]; Print[n, " ", r]; Continue, {n, 0, 100}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|