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Search: id:A005843
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| A005843 |
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The even numbers: a(n) = 2n.
(Formerly M0985)
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+0
83
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| 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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-2, -4, -6, -8, -10, -12, -14, ... are the trivial zeros of the Riemann zeta function. - Vivek Suri (vsuri(AT)jhu.edu), Jan 24 2008
Numbers of carbons in the oligomers of acetylene. - Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Oct 27 2005
Excluding the first two terms, this sequenc is the same as the number of carbons in the oligomers of cyclobutane sharing a common edge. - Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Apr 05 2006
If a 2-set Y and an (n-2)-set Z are disjoint subsets of an n-set X then a(n-2) is the number of 2-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Sep 19 2007
A134452(a(n)) = 0; A134451(a(n)) = 2 for n>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 27 2007
Omitting the initial zero gives the number of prime divisors with multiplicity of product of terms of n-th row of A077553. - Ray Chandler (rayjchandler(AT)sbcglobal.net), Aug 21 2003
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 2.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..10000
Milan Janjic, Two Enumerative Functions
Tanya Khovanova, Recursive Sequences
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Tanya Khovanova, Recursive Sequences
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Hamiltonian Circuit
Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros.
Index entries for "core" sequences
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FORMULA
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G.f.: 2*x/(1-x)^2.
Inverse binomial transform of A036289, n*2^n. - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Jan 13 2006
a(0)=0, a(1)=2, a(n)=2a(n-1)-a(n-2). - Jaume Oliver i Lafont (joliverlafont(AT)gmail.com), May 07 2008
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MAPLE
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A005843 := n->2*n;
A005843:=2/(z-1)**2; [S. Plouffe in his 1992 dissertation.]
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PROGRAM
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(MAGMA) [ 2*n : n in [0..100]];
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CROSSREFS
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Cf. A000027, A005408.
Cf. A001358, A005843, A077553, A077554, A077555, A002024, A087112.
Sequence in context: A087113 A004275 A119432 this_sequence A076032 A004277 A122080
Adjacent sequences: A005840 A005841 A005842 this_sequence A005844 A005845 A005846
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KEYWORD
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easy,core,nonn,nice
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AUTHOR
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njas
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