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A101101 a(1)=1, a(2)=5, and a(n)=6 for n>=3. 3
1, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Previous name was: The first summation of row 3 of Euler's triangle - a row that will recursively accumulate to the power of 3.

LINKS

Table of n, a(n) for n=1..80.

D. J. Pengelley, The bridge between the continuous and the discrete via original sources in Study the Masters: The Abel-Fauvel Conference [pdf], Kristiansand, 2002, (ed. Otto Bekken et al.), National Center for Mathematics Education, University of Gothenburg, Sweden, in press.

C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.  [broken link: domain now owned by a domain grabber]

Eric Weisstein, Link to section of MathWorld: Worpitzky's Identity of 1883.

Eric Weisstein, Link to section of MathWorld: Eulerian Number.

Eric Weisstein, Link to section of MathWorld: Nexus number.

Eric Weisstein, Link to section of MathWorld: Finite Differences.

Index entries for linear recurrences with constant coefficients, signature (1).

FORMULA

G.f.: x*(1+4*x+x^2)/(1-x). - L. Edson Jeffery, Jan 29 2012

MATHEMATICA

MagicNKZ=Sum[(-1)^j*Binomial[n+1-z, j]*(k-j+1)^n, {j, 0, k+1}]; Table[MagicNKZ, {n, 3, 3}, {z, 1, 1}, {k, 0, 34}] (* OR *)

SeriesAtLevelR = Sum[Eulerian[n, i - 1]*Binomial[n + x - i + r, n + r], {i, 1, n}]; Table[SeriesAtLevelR, {n, 3, 3}, {r, -3, -3}, {x, 4, 35}]

Join[{1, 5}, LinearRecurrence[{1}, {6}, 78]] (* Ray Chandler, Sep 23 2015 *)

CROSSREFS

Within the "cube" of related sequences with construction based upon MaginNKZ formula, with n downward, k rightward and z backward:

Before: this_sequence, A008458, A003215, A000578, A000537, A024166 or A024166, A101094, A101097, A101102.

Above: this_sequence, below: A101104, A101100.

Within the "cube" of related sequences with construction based upon SeriesAtLevelR formula, with n downward, x rightward and r backward:

Above: this_sequence, below: A101103, A101096.

Sequence in context: A004553 A074826 A018246 * A046786 A035591 A256683

Adjacent sequences:  A101098 A101099 A101100 * A101102 A101103 A101104

KEYWORD

easy,nonn,uned

AUTHOR

Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004

EXTENSIONS

I wish the sequence was as interesting as the list of references! - N. J. A. Sloane

New name from Joerg Arndt, Nov 30 2014

STATUS

approved

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Last modified November 18 12:35 EST 2019. Contains 329261 sequences. (Running on oeis4.)