cp's OEIS Frontend

A101101 a(1)=1, a(2)=5, and a(n)=6 for n >= 3.

%I A101101 #34 Feb 16 2025 08:32:55
%S A101101 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,
%T A101101 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,
%U A101101 6,6,6,6,6,6,6,6,6,6,6,6
%N A101101 a(1)=1, a(2)=5, and a(n)=6 for n >= 3.
%C A101101 Previous name was: The first summation of row 3 of Euler's triangle - a row that will recursively accumulate to the power of 3.
%C A101101 Decimal expansion of 47/30. - _Elmo R. Oliveira_, Aug 09 2024
%H A101101 D. J. Pengelley, <a href="http://www.math.nmsu.edu/~davidp/bridge.pdf">The bridge between the continuous and the discrete via original sources in Study the Masters: The Abel-Fauvel Conference</a> [pdf], Kristiansand, 2002, (ed. Otto Bekken et al.), National Center for Mathematics Education, University of Gothenburg, Sweden, in press.
%H A101101 C. Rossiter, <a href="http://noticingnumbers.net/300SeriesCube.htm">Depictions, Explorations and Formulas of the Euler/Pascal Cube</a>.  [broken link: domain now owned by a domain grabber]
%H A101101 Eric Weisstein, Link to section of MathWorld: <a href="https://mathworld.wolfram.com/WorpitzkysIdentity.html">Worpitzky's Identity of 1883</a>.
%H A101101 Eric Weisstein, Link to section of MathWorld: <a href="https://mathworld.wolfram.com/EulerianNumber.html">Eulerian Number</a>.
%H A101101 Eric Weisstein, Link to section of MathWorld: <a href="https://mathworld.wolfram.com/NexusNumber.html">Nexus number</a>.
%H A101101 Eric Weisstein, Link to section of MathWorld: <a href="https://mathworld.wolfram.com/FiniteDifference.html">Finite Differences</a>.
%H A101101 Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, <a href="https://ceur-ws.org/Vol-3792/paper19.pdf">Integer sequences from k-iterated line digraphs</a>, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
%H A101101 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A101101 G.f.: x*(1+4*x+x^2)/(1-x). - _L. Edson Jeffery_, Jan 29 2012
%t A101101 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 *)
%t A101101 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}]
%t A101101 Join[{1, 5},LinearRecurrence[{1},{6},78]] (* _Ray Chandler_, Sep 23 2015 *)
%Y A101101 Within the "cube" of related sequences with construction based upon MaginNKZ formula, with n downward, k rightward and z backward:
%Y A101101 Before: this_sequence, A008458, A003215, A000578, A000537, A024166 or A024166, A101094, A101097, A101102.
%Y A101101 Above: this_sequence, below: A101104, A101100.
%Y A101101 Within the "cube" of related sequences with construction based upon SeriesAtLevelR formula, with n downward, x rightward and r backward:
%Y A101101 Above: this_sequence, below: A101103, A101096.
%K A101101 easy,nonn,uned
%O A101101 1,2
%A A101101 Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004
%E A101101 I wish the sequence was as interesting as the list of references! - _N. J. A. Sloane_
%E A101101 New name from _Joerg Arndt_, Nov 30 2014