The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A356113

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A356113

Triangle read by rows. T(n, k) = A355776(n, k) + A355777(n, k). Refining A174159, the Euler minus Narayana/Catalan triangle.
(history; published version)

#12 by Peter Luschny at Tue Aug 23 05:21:37 EDT 2022

STATUS

editing

approved

#11 by Peter Luschny at Tue Aug 23 05:21:34 EDT 2022

EXAMPLE

[0] [1];

[1] [1];

[2] [1, 1];

[3] [1, 5, 1];

[4] [1, [10, 6], 16, 1];

[5] [1, [17, 25], [54, 58], 42, 1];

[6] [1, [26, 46, 27], [137, 354, 63], [224, 330], 99, 1];

[7] [1, [37, 77, 105], [291, 906, 513, 567], [817, 2883, 957],[811, 1466], 219, 1];

STATUS

approved

editing

#10 by Michael De Vlieger at Sun Jul 31 08:14:24 EDT 2022

STATUS

proposed

approved

#9 by Peter Luschny at Sun Jul 31 07:41:06 EDT 2022

STATUS

editing

proposed

#8 by Peter Luschny at Sun Jul 31 07:38:37 EDT 2022

CROSSREFS

Cf. A355776, A355777, A356118 (row sums), A174159 (parent reduced triangle).

#7 by Peter Luschny at Sun Jul 31 03:47:49 EDT 2022

LINKS

Peter Luschny, <a href="https://github.com/PeterLuschny/PermutationsWithLehmer/blob/main/PermutationsWithLehmer.ipynb">Permutations with Lehmer</a>, a SageMath Jupyter Notebook.

#6 by Peter Luschny at Fri Jul 29 04:25:43 EDT 2022

NAME

Triangle read by rows. T(n, k) = A355776(n, k) + A355777(n, k). Refining A174159, the Euler minus Narayana/Catalan triangle.

#5 by Peter Luschny at Thu Jul 28 12:22:02 EDT 2022

NAME

Triangle read by rows. T(n, k) = A355776(n, k) + A355777(n, k).

DATA

1, 1, 1, 1, 1, 5, 1, 1, 10, 6, 16, 1, 1, 17, 25, 54, 58, 42, 1, 1, 26, 46, 27, 137, 354, 63, 224, 330, 99, 1, 1, 37, 77, 105, 291, 906, 513, 567, 817, 2883, 957, 811, 1466, 219, 1, 1, 50, 120, 188, 108, 548, 2020, 2632, 1508, 1682, 2356, 10116, 5574, 11724, 978, 4184, 18128, 8436, 2722, 5668, 466, 1

OFFSET

1,5

0,6

EXAMPLE

[0] [1]

[2] [1, 1]

[3] [1, 5, 1]

[4] [1, [10, 6], 16, 1]

[5] [1, [17, 25], [54, 58], 42, 1]

[6] [1, [26, 46, 27], [137, 354, 63], [224, 330], 99, 1]

[7] [1, [37, 77, 105], [291, 906, 513, 567], [817, 2883, 957],[811, 1466], 219, 1]

PROG

(SageMath)

for n in range(8):

print([n], [A355776(n, k) + A355777(n, k)

for k in range(number_of_partitions(n))])

CROSSREFS

Cf. A355776, A355777, A356118 (row sums), A174159 (parent triangle).

KEYWORD

nonn,tabl,tabf,changed

#4 by Peter Luschny at Thu Jul 28 04:50:30 EDT 2022

CROSSREFS

Cf. A356118 (row sums), A174159 (parent triangle).

#3 by Peter Luschny at Thu Jul 28 04:41:10 EDT 2022

NAME

allocated for Peter LuschnyTriangle read by rows

DATA

1, 1, 1, 1, 5, 1, 1, 10, 6, 16, 1, 1, 17, 25, 54, 58, 42, 1

OFFSET

1,5

EXAMPLE

Triangle T(n, k) begins:

[1] [1]

[2] [1, 1]

[3] [1, 5, 1]

[4] [1, [10, 6], 16, 1]

[5] [1, [17, 25], [54, 58], 42, 1]

KEYWORD

allocated

nonn,tabl

AUTHOR

Peter Luschny, Jul 28 2022

STATUS

approved

editing