

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
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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 AbelFauvel 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)/(1x).  L. Edson Jeffery, Jan 29 2012


MATHEMATICA

MagicNKZ=Sum[(1)^j*Binomial[n+1z, j]*(kj+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



