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A014781
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Seidel's triangle, read by rows.
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3
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1, 1, 1, 1, 2, 1, 2, 3, 3, 8, 6, 3, 8, 14, 17, 17, 56, 48, 34, 17, 56, 104, 138, 155, 155, 608, 552, 448, 310, 155, 608, 1160, 1608, 1918, 2073, 2073, 9440, 8832, 7672, 6064, 4146, 2073, 9440, 18272, 25944, 32008, 36154, 38227
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OFFSET
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1,5
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COMMENTS
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Named after the German mathematician Philipp Ludwig von Seidel (1821-1896). - Amiram Eldar, Jun 13 2021
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REFERENCES
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Qiongqiong Pan and Jiang Zeng, Cycles of even-odd drop permutations and continued fractions of Genocchi numbers, arXiv:2108.03200 [math.CO], 2021.
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LINKS
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EXAMPLE
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Triangle begins:
1;
1;
1, 1;
2, 1;
2, 3, 3;
8, 6, 3;
8, 14, 17, 17;
56, 48, 34, 17;
56, 104, 138, 155, 155;
608, 552, 448, 310, 155;
608, 1160, 1608, 1918, 2073, 2073;
9440, 8832, 7672, 6064, 4146, 2073;
...
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MATHEMATICA
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max = 13; T[1, 1] = 1; T[n_, k_] /; 1 <= k <= (n+1)/2 := T[n, k] = If[EvenQ[n], Sum[T[n-1, i], {i, k, max}], Sum[T[n-1, i], {i, 1, k}]]; T[_, _] = 0; Table[T[n, k], {n, 1, max}, {k, 1, (n+1)/2}] // Flatten (* Jean-François Alcover, Nov 18 2016 *)
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PROG
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(SageMath) # Algorithm of L. Seidel (1877)
# n -> Prints first n rows of the triangle
D = []; [D.append(0) for i in (0..n)]; D[1] = 1
b = True
for i in(0..n) :
h = (i-1)//2 + 1
if b :
for k in range(h-1, 0, -1) : D[k] += D[k+1]
else :
for k in range(1, h+1, 1) : D[k] += D[k-1]
b = not b
if i>0 : print [D[z] for z in (1..h)]
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CROSSREFS
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KEYWORD
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tabf,nonn
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AUTHOR
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EXTENSIONS
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More terms from Mike Domaratzki (mdomaratzki(AT)alumni.uwaterloo.ca), Nov 18 2001
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STATUS
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approved
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