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).

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, 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, 2, 2, 232, 88, 141, 66, 33, 40, 24, 12, 14, 8, 4, 4, 2, 1, 376, 143, 230, 108, 54, 66

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..77.

Kival Ngaokrajang, Illustration of initial terms, T(n,k) for n = 0..10, k = 0..13

Example

Irreuglar triangle begins:
n/k  0  1  2  3  4  5  6  7  8 ...
0   1
1   2
2   4  1
3   7  2  2
4  12  4  5  2  1
5  20  7 10  4  2  2
6  33 12 18  8  4  4  2  1
7  54 20 31 14  7  8  4  2  2
8  88 33 52 24 12 14  8  4  4
...

Prog

(PARI)
{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, ", ")))}

Crossrefs

Cf. A255870, A032766, A000071, A006327.

Sequence in context: A302541 A119303 A374116 * A207610 A207616 A105552

Adjacent sequences: A256104 A256105 A256106 * A256108 A256109 A256110

Keyword

nonn,tabf

Author

Kival Ngaokrajang, Mar 14 2015

Status

approved