A348175 Irregular table T(n,k) read by rows: T(n,k) = T(n-1,k/2) when k is even and 3*T(n-1,(k-1)/2) + 2^(n-1) when k is odd. T(0,0) = 0 and 0 <= k <= 2^n-1.

0, 0, 1, 0, 2, 1, 5, 0, 4, 2, 10, 1, 7, 5, 19, 0, 8, 4, 20, 2, 14, 10, 38, 1, 11, 7, 29, 5, 23, 19, 65, 0, 16, 8, 40, 4, 28, 20, 76, 2, 22, 14, 58, 10, 46, 38, 130, 1, 19, 11, 49, 7, 37, 29, 103, 5, 31, 23, 85, 19, 73, 65, 211

Offset: 0

Author

Ryan Brooks, Oct 04 2021

Keywords

• nonn
• tabf

Examples

			n\k 0  1  2  3  4  5  6  7
0   0
1   0  1
2   0  2  1  5
3   0  4  2 10  1  7  5 19
		

Crossrefs

Cf. A001047 (right diagonal), A002697 (row sums), A119733.

Cf. A133457 (binary exponents).

Programs

Mathematica

T[0, 0] = 0; T[n_, k_] := T[n, k] = If[EvenQ[k], T[n - 1, k/2], 3*T[n - 1, (k - 1)/2] + 2^(n - 1)]; Table[T[n, k], {n, 0, 5}, {k, 0, 2^n - 1}] // Flatten (* Amiram Eldar, Oct 11 2021 *)

PARI

T(n, k) = if ((n==0) && (k==0), 0, if (k%2, 3*T(n-1,(k-1)/2) + 2^(n-1), T(n-1,k/2)));
tabf(nn) = for (n=0, nn, for (k=0, 2^n-1, print1(T(n,k), ", ")); print); \\ Michel Marcus, Oct 18 2021

PARI

T(n,k) = my(ret=0); for(i=0,n-1, if(bittest(k,n-1-i), ret=3*ret+1<Kevin Ryde, Oct 22 2021

Formula

T(n,k) = T(n-1,k/2) for k being even.

T(n,k) = 3*T(n-1,(k-1)/2) + 2^(n-1) for k being odd.

T(n,k) = 2*T(n-1,k) for 0 <= k <= 2^(n-1) - 1.

T(n,k) = Sum_{i=0..r} 2^(n-1-e[i]) * 3^i where binary expansion k = 2^e[0] + 2^e[1] + ... + 2^e[r] with ascending e[0] < e[1] < ... < e[r] (A133457). - Kevin Ryde, Oct 22 2021