OFFSET

1,1

COMMENTS

LINKS

Wikipedia, Arithmetic sequence

EXAMPLE

Since A371663(17) = 45 and from a 45-gon 8 arithmetic progressions p_i(k) can formed from all its interior angles (all integer, in degrees), a(17) = 8. The 8 sequences are: p_1(k) = 172, p_2(k) = k + 150, p_3(k) = 2k + 128, p_4(k) = 3k + 106, p_5(k) = 4k + 84, p_6(k) = 5k + 62, p_7(k) = 6k + 40, p_8(k) = 7k + 18, for integers k with 0 <= k <= 44.

Since A371663(19) = 60 and from a 60-gon 3 arithmetic progressions p_i(k) can formed from all its interior angles (all integer, in degrees), a(19) = 3. The 3 sequences are: p_1(k) = 174, p_2(k) = 2k + 115, p_3(k) = 4k + 56, for integers k with 0 <= k <= 15.

Since A371663(10) = 16 and from a 16-gon 10 arithmetic progressions p_i(k) can formed from all its interior angles (all integer, in degrees), a(10) = 10. The 10 sequences are: p_1(k) = k + 150, p_2(k) = 3k + 135, p_3(k) = 5k + 120, p_4(k) = 7k + 105, p_5(k) = 9k + 90, p_6(k) = 11k + 75, p_7(k) = 13k + 60, p_8(k) = 15k + 45, p_9(k) = 17k + 30, p_10(k) = 19k + 15 for integers k with 0 <= k <= 15.

MAPLE

A371664:=proc(n)

local a, L;

L:=[3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360];

if (L[n]-2)*180/L[n]=floor((L[n]-2)*180/L[n]) then

if L[n] mod 2 = 1 then

a:=ceil(((L[n]-2)*360/L[n])/(L[n]-1))

else a:=ceil(((L[n]-2)*180/L[n])/(L[n]-1))

fi;

elif (L[n]-2)*360/L[n]=floor((L[n]-2)*360/L[n]) and L[n] mod 2 = 0 then

a:=ceil(((L[n]-2)*360/L[n]-L[n]+1)/(2*(L[n]-1)))

fi;

return a;

end proc;

seq(A371664(n), n=1..27);

CROSSREFS

KEYWORD

fini,full,nonn

AUTHOR

Felix Huber, Apr 04 2024

STATUS

approved