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A348175
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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.
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0
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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
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OFFSET
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0,5
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LINKS
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FORMULA
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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
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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<<i)); ret; \\ Kevin Ryde, Oct 22 2021
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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