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Central elements in writing first the numerator and then the denominator (left to right) of Leibniz's harmonic-like triangle.
+10
7
1, 1, 5, 6, 31, 30, 209, 140, 1471, 630, 10625, 2772
EXAMPLE
1/1; --> 1 1
1/2, 1/2; -->
1/3, 5/6, 1/3; --> 5 6
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;
Elements to the right of the central elements in writing first the denominator and then the numerator(left to right) of Leibniz's harmonic-like triangle.
+10
5
2, 1, 3, 1, 12, 7, 4, 1, 20, 9, 5, 1, 60, 49, 30, 11, 6, 1, 105, 71, 42, 13, 7, 1, 280, 351, 168, 97, 56, 15, 8, 1, 504, 545, 252, 127, 72, 17, 9, 1, 1260, 2561, 840, 799, 360, 161, 90, 19, 10, 1, 2310, 4159, 1320, 1121, 495, 199, 110, 21, 11, 1
EXAMPLE
1/1; -->
1/2, 1/2; --> 2 1
1/3, 5/6, 1/3; --> 3 1
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;
Nontrivial numbers of the elements to the right of the central elements in writing first the denominator and then the numerator(left to right) of Leibniz's harmonic-like triangle. That is, the nontrivial elements of A137764.
+10
4
2, 3, 12, 7, 4, 20, 9, 5, 60, 49, 30, 11, 6, 105, 71, 42, 13, 7, 280, 351, 168, 97, 56, 15, 8, 504, 545, 252, 127, 72, 17, 9, 1260, 2561, 840, 799, 360, 161, 90, 19, 10, 2310, 4159, 1320, 1121, 495, 199, 110, 21, 11
EXAMPLE
1/1; -->
1/2, 1/2; --> 2
1/3, 5/6, 1/3; --> 3
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;
Elements to the right of the central element in writing first the numerator and then the denominator (left to right) of Leibniz's harmonic-like triangle.
+10
3
1, 2, 1, 3, 7, 12, 1, 4, 9, 20, 1, 5, 49, 60, 11, 30, 1, 6, 71, 105, 13, 42, 1, 7, 351, 280, 97, 168, 15, 56, 1, 8, 545, 504, 127, 252, 17, 72, 1, 9, 2561, 1260, 799, 840, 161, 360, 19, 90, 1, 10, 4159, 2310, 1121, 1320, 199, 495, 21, 110, 1, 11
EXAMPLE
1/1; -->
1/2, 1/2; --> 1 2
1/3, 5/6, 1/3; --> 1 3
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;
CROSSREFS
Cf. A046201, A046204, A046205, A046206, A046208, A046212, A137752, A137753, A137754, A137755, A137756, A137757, A137758, A137759, A137760, A137761, A137762, A137763, A137764, A137765.
Nontrivial numbers of the elements to the right of the central elements in writing first the numerator and then the denominator (left to right) of Leibniz's harmonic-like triangle.
+10
2
2, 3, 7, 12, 4, 9, 20, 5, 49, 60, 11, 30, 6, 71, 105, 13, 42, 7, 351, 280, 97, 168, 15, 56, 8, 545, 504, 127, 252, 17, 72, 9, 2561, 1260, 799, 840, 161, 360, 19, 90, 10, 4159, 2310, 1121, 1320, 199, 495, 21, 110, 11
EXAMPLE
1/1; -->
1/2, 1/2; --> 2
1/3, 5/6, 1/3; --> 3
1/4, 7/12, 7/12, 1/4; --> 7 12
1/5, 9/20, 31/30, 9/20, 1/5; --> ...
CROSSREFS
Cf. A046201, A046204, A046205, A046206, A046208, A046212, A137752, A137753, A137754, A137755, A137756, A137757, A137758, A137759, A137760, A137761, A137762, A137763, A137764, A137765, A137766.
Nontrivial odd numbers in writing first the numerator and then the denominator (left to right) of Leibniz's harmonic-like triangle.
+10
1
3, 5, 3, 7, 7, 5, 9, 31, 9, 5, 11, 49, 49, 11, 7, 13, 71, 105, 209, 71, 105, 13, 7, 15, 97, 351, 351, 97, 15, 9, 17, 127, 545, 1471, 545, 127, 17, 9, 19, 161, 799, 2561, 2561, 799, 161, 19, 11, 21, 199, 495, 1121, 4159, 10625, 4159, 1121, 199, 495, 21, 11
EXAMPLE
1/1; -->
1/2, 1/2; -->
1/3, 5/6, 1/3; --> 3 5 3
1/4, 7/12, 7/12, 1/4; --> 7 7
1/5, 9/20, 31/30, 9/20, 1/5; --> ...
CROSSREFS
Cf. A046212, A137752, A137753, A137754, A137755, A137756, A137757, A137758, A137759, A137760, A137761, A137762, A137763, A137764, A137765, A137766, A137767.
Nontrivial odd numbers in writing first the denominator and then the numerator (left to right) of Leibniz's harmonic-like triangle.
+10
0
3, 5, 3, 7, 7, 5, 9, 31, 9, 5, 11, 49, 49, 11, 7, 13, 105, 71, 209, 105, 71, 13, 7, 15, 97, 351, 351, 97, 15, 9, 17, 127, 545, 1471, 545, 127, 17, 9, 19, 161, 799, 2561, 2561, 799, 161, 19, 11, 21, 495, 199, 1121, 4159, 10625, 4159, 1121, 495, 199, 21, 11
EXAMPLE
1/1; -->
1/2, 1/2; -->
1/3, 5/6, 1/3; --> 3 5
1/4, 7/12, 7/12, 1/4; --> 7 7
1/5, 9/20, 31/30, 9/20, 1/5;
CROSSREFS
Cf. A046212, A137752, A137753, A137754, A137755, A137756, A137757, A137758, A137759, A137760, A137761, A137762, A137763, A137764, A137765, A137766, A137767: A137768.
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