The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A026300

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A026300

Motzkin triangle, T, read by rows; T(0,0) = T(1,0) = T(1,1) = 1; for n >= 2, T(n,0) = 1, T(n,k) = T(n-1,k-2) + T(n-1,k-1) + T(n-1,k) for k = 1,2,...,n-1 and T(n,n) = T(n-1,n-2) + T(n-1,n-1).
(history; published version)

#105 by Peter Luschny at Sun Feb 26 08:26:50 EST 2023

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#104 by Joerg Arndt at Sun Feb 26 06:56:55 EST 2023

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proposed

reviewed

#103 by Peter Bala at Sun Feb 26 05:51:20 EST 2023

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editing

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#102 by Peter Bala at Sun Feb 26 05:49:14 EST 2023

FORMULA

The n-th row polynomial R(n,x) equals the n-th degree Taylor polynomial of the function (1 - x^2)*(1 + x + x^2)^n expanded about the point x = 0. - Peter Bala, Feb 26 2023

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editing

#101 by Peter Luschny at Wed May 19 06:50:03 EDT 2021

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editing

approved

#100 by Peter Luschny at Wed May 19 06:49:58 EDT 2021

EXAMPLE

[0] 1;

[1] 1 , 1;

[2] 1 , 2, 2;

[3] 1 , 3, 5, 4;

[4] 1 , 4, 9, 12, 9;

[5] 1 , 5, 14, 25, 30, 21;

[6] 1, 6, 20, 44, 69, 76, 51;

...

[7] 1, 7, 27, 70, 133, 189, 196, 127;

[8] 1, 8, 35, 104, 230, 392, 518, 512, 323;

[9] 1, 9, 44, 147, 369, 726, 1140, 1422, 1353, 835.

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approved

editing

#99 by Susanna Cuyler at Fri Mar 05 21:44:30 EST 2021

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proposed

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#98 by Michael De Vlieger at Fri Mar 05 19:51:39 EST 2021

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#97 by Michael De Vlieger at Fri Mar 05 19:51:37 EST 2021

LINKS

M. János Uray, <a href="https://urayjanos.web.elte.hu/pub/expol-family.pdf">A family of barely expansive polynomials</a>, Eötvös Loránd University (Budapest, Hungary, 2020).

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approved

editing

#96 by Sean A. Irvine at Tue Apr 23 19:37:21 EDT 2019

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reviewed

approved