cp's OEIS Frontend

A256107 Irregular triangle read by rows, T(n,k) is the number of pentagrams on the k layers at n iterations of a pentagram fractal (see comment).

%I A256107 #19 Mar 27 2015 21:20:09
%S A256107 1,2,4,1,7,2,2,12,4,5,2,1,20,7,10,4,2,2,33,12,18,8,4,4,2,1,54,20,31,
%T A256107 14,7,8,4,2,2,88,33,52,24,12,14,8,4,4,2,1,143,54,86,40,20,24,14,7,8,4,
%U A256107 2,2,232,88,141,66,33,40,24,12,14,8,4,4,2,1,376,143,230,108,54,66
%N A256107 Irregular triangle read by rows, T(n,k) is the number of pentagrams on the k layers at n iterations of a pentagram fractal (see comment).
%C A256107 Refer to A255870, the number of pentagrams on one side of the outer layer (including pentagrams on two vertices) at n iterations would be T(n,0), the next layers k >= 1 T(n,k) are the number of pentagrams toward the center. For k >= 2, the row length is A032766. The first differences of A255870 = 5*(rows sum - 1). T(n,k) = A000071 with a shift for k = 0 or k mod 3 = 1. T(n,2) = A006327 with a shift. For k >= 3, T(n,k) = 2*A000071 with a shift for k mod 3 = 0 or 2. See illustration in the links.
%H A256107 Kival Ngaokrajang, <a href="/A256107/a256107_1.pdf">Illustration of initial terms</a>, <a href="/A256107/a256107_2.pdf">T(n,k) for n = 0..10, k = 0..13</a>
%e A256107 Irreuglar triangle begins:
%e A256107 n/k  0  1  2  3  4  5  6  7  8 ...
%e A256107 0   1
%e A256107 1   2
%e A256107 2   4  1
%e A256107 3   7  2  2
%e A256107 4  12  4  5  2  1
%e A256107 5  20  7 10  4  2  2
%e A256107 6  33 12 18  8  4  4  2  1
%e A256107 7  54 20 31 14  7  8  4  2  2
%e A256107 8  88 33 52 24 12 14  8  4  4
%e A256107 ...
%o A256107 (PARI)
%o A256107 {for(n=0, 20, if(n<2, lk=0, lk=floor(3*(n-2)/2)+1); for (k=0, lk, if(k<>0, if(k<>2, if(Mod(k,3)==1, t=fibonacci(n+1-2*(k-1)/3)-1, t=2*(fibonacci(n+2-ceil((2*k+1)/3))-1)), t=fibonacci(n+2)-3), t=fibonacci(n+3-2*k/3)-1); print1(t, ", ")))}
%Y A256107 Cf. A255870, A032766, A000071, A006327.
%K A256107 nonn,tabf
%O A256107 0,2
%A A256107 _Kival Ngaokrajang_, Mar 14 2015