The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A201165 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A201165

Triangle read by rows: Pascal's triangle (A007318) times the Fibonacci triangle (A139375).
(history; published version)

#21 by Susanna Cuyler at Fri Apr 03 07:52:40 EDT 2020

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reviewed

approved

#20 by Wesley Ivan Hurt at Fri Apr 03 07:49:51 EDT 2020

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proposed

reviewed

#19 by Jean-François Alcover at Fri Apr 03 06:01:14 EDT 2020

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editing

proposed

#18 by Jean-François Alcover at Fri Apr 03 06:01:02 EDT 2020

MATHEMATICA

F[n_, k_] := If[k == 0, Fibonacci[n+1], k Sum[Fibonacci[i+1] Binomial[2(n-i)-k-1, n-i-1]/(n-i), {i, 0, n-k}]];

T[n_, k_] := Sum[Binomial[n, j] F[j, k], {j, k, n}];

Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 03 2020 *)

STATUS

approved

editing

#17 by Bruno Berselli at Wed Mar 18 14:51:27 EDT 2020

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reviewed

approved

#16 by Joerg Arndt at Wed Mar 18 13:01:23 EDT 2020

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proposed

reviewed

#15 by Michel Marcus at Wed Mar 18 12:17:23 EDT 2020

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editing

proposed

#14 by Michel Marcus at Wed Mar 18 12:17:19 EDT 2020

REFERENCES

He, Tian-Xiao, and Sprugnoli, Renzo; Sequence characterization of Riordan arrays. Discrete Math. 309 (2009), no. 12, 3962-3974.

LINKS

Tian-Xiao He and Renzo Sprugnoli, <a href="https://doi.org/10.1016/j.disc.2008.11.021">Sequence characterization of Riordan arrays</a>, Discrete Math. 309 (2009), no. 12, 3962-3974.

FORMULA

T(n,k) = sum_Sum_{j=k..n} A007318(n,j)*A139375(j,k).

STATUS

approved

editing

#13 by R. J. Mathar at Tue Jul 09 13:48:08 EDT 2013

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proposed

approved

#12 by R. J. Mathar at Tue Jul 09 13:40:36 EDT 2013

STATUS

editing

proposed