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Square array A(row>=0, col>=0) = (A166092(row,col)-3)/4, listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...
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%I #6 Dec 14 2023 14:24:42

%S 0,1,2,3,79,4,5,151,8,103,7,175,14,409,22,9,223,15,589,43,10,11,265,

%T 25,998,143,31,12,13,275,32,1297,157,73,20,16,17,283,62,1364,182,158,

%U 55,28,6,19,361,69,1891,293,164,183,34,26,52,21,373,74,1952,397,401

%N Square array A(row>=0, col>=0) = (A166092(row,col)-3)/4, listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...

%C Note: This is not a permutation of nonnegative integers, as for some odd n, A166040(n) gets even value, the first example being A166040(49)=32, thus 24 (= (49-1)/2) is missing from here, and correspondingly, 99 (= 2*49 + 1) is missing from A166092. Sequence A165602 gives the natural numbers missing from this table.

%H A. Karttunen, <a href="/A166091/b166091.txt">Table of n, a(n) for n = 0..10010</a>

%e The top left corner of the array:

%e 0, 1, 3, 5, 7, 9, ...

%e 2, 79, 151, 175, 223, 265, ...

%e 4, 8, 14, 15, 25, 32, ...

%e 103, 409, 589, 998, 1297, 1364, ...

%e 22, 43, 143, 157, 182, 293, ...

%o (MIT/GNU Scheme)

%o (define (A166091 n) (A166091bi (A025581 n) (A002262 n)))

%o (define (A166091bi n k) (let ((m (A005408 k))) (let loop ((i 0) (n n)) (cond ((= m (A166086 i)) (if (zero? n) i (loop (1+ i) (-1+ n)))) (else (loop (1+ i) n))))))

%Y See A166092. The leftmost column: A166094. The first five rows: A165468, A166052, A166054, A166056, A166058. Cf. also A112060.

%K nonn,tabl

%O 0,3

%A _Antti Karttunen_, Oct 08 2009