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Array A read by upward antidiagonals in which the entry A(n,k) = A371092(A371100(n, k)), n,k >= 1.
7

%I #8 Apr 19 2024 15:03:33

%S 1,1,3,1,2,3,1,3,1,6,1,2,3,5,2,1,3,1,6,4,9,1,2,3,5,2,8,6,1,3,1,6,4,9,

%T 2,12,1,2,3,5,2,8,6,11,1,1,3,1,6,4,9,2,12,7,15,1,2,3,5,2,8,6,11,1,14,

%U 9,1,3,1,6,4,9,2,12,7,15,4,18,1,2,3,5,2,8,6,11,1,14,9,17,5,1,3,1,6,4,9,2,12,7,15,4,18,10,21

%N Array A read by upward antidiagonals in which the entry A(n,k) = A371092(A371100(n, k)), n,k >= 1.

%C A(n, k) gives the column index of A371100(n, k) in array A257852.

%F A(n, k) = A371092(A371100(n, k)).

%F A(n, k) = A(n+2, k).

%e The array begins:

%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

%e ---+--------------------------------------------------------------------

%e 1 | 1, 3, 3, 6, 2, 9, 6, 12, 1, 15, 9, 18, 5, 21, 12, 24, 4, 27, ...

%e 2 | 1, 2, 1, 5, 4, 8, 2, 11, 7, 14, 4, 17, 10, 20, 1, 23, 13, 26, ...

%e 3 | 1, 3, 3, 6, 2, 9, 6, 12, 1, 15, 9, 18, 5, 21, 12, 24, 4, 27, ...

%e 4 | 1, 2, 1, 5, 4, 8, 2, 11, 7, 14, 4, 17, 10, 20, 1, 23, 13, 26, ...

%e 5 | 1, 3, 3, 6, 2, 9, 6, 12, 1, 15, 9, 18, 5, 21, 12, 24, 4, 27, ...

%e 6 | 1, 2, 1, 5, 4, 8, 2, 11, 7, 14, 4, 17, 10, 20, 1, 23, 13, 26, ...

%e 7 | 1, 3, 3, 6, 2, 9, 6, 12, 1, 15, 9, 18, 5, 21, 12, 24, 4, 27, ...

%e 8 | 1, 2, 1, 5, 4, 8, 2, 11, 7, 14, 4, 17, 10, 20, 1, 23, 13, 26, ...

%e ...

%o (PARI)

%o up_to = 105;

%o A000265(n) = (n>>valuation(n,2));

%o A371092(n) = floor((A000265(1+(3*n))+5)/6);

%o A371100sq(n,k) = 4^n*(6*k - 3 - 2*(-1)^n) + (4^n - 1)/3;

%o A371101sq(n,k) = A371092(A371100sq(n,k));

%o A371101list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A371101sq((a-(col-1)),col))); (v); };

%o v371101 = A371101list(up_to);

%o A371101(n) = v371101[n];

%Y Cf. A257852, A371092, A371100.

%K nonn,tabl

%O 1,3

%A _Antti Karttunen_, Apr 19 2024