The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 11 18:37 EDT 2020. Contains 336428 sequences. (Running on oeis4.)