Search: id:A006261
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%I A006261 M1126
%S A006261 1,2,4,8,16,32,63,120,219,382,638,1024,1586,2380,3473,4944,6885,
%T A006261 9402,12616,16664,21700,27896,35443,44552,55455,68406,83682,101584,
%U A006261 122438,146596,174437,206368,242825,284274,331212,384168,443704
%N A006261 Sum_{ k = 0..5 } C(n,k).
%C A006261 a(n) is the sum of the first six terms of the nth row in Pascal's triangle. 
               [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Jan 19 2009]
%C A006261 Also the interpolating polynomial for the divisors of 32: {a(k):0<=k<6}={1,
               2,4,8,16,32}. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jun 17 2009]
%D A006261 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006261 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 72, Problem 2.
%D A006261 M. L. Cornelius, Variations on a geometric progression, Mathematics in 
               School, 4 (No. 3, May 1975), p. 32.
%H A006261 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A006261 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A006261 R. Zumkeller, <a href="a161700.txt">Enumerations of Divisors</a> [From 
               Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009]
%F A006261 a(n)=binomial(n+1, 5)+binomial(n+1, 3)+binomial(n+1, 1). - Len Smiley 
               (smiley(AT)math.uaa.alaska.edu), Oct 20 2001
%F A006261 G.f.: 1-4x+7x^2-6x^3+3x^4/(1-x)^6 [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Jan 19 2009]
%F A006261 a(n) = (n^5 - 5*n^4 + 25*n^3 + 5*n^2 + 94*n + 120)/120. [From Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009]
%e A006261 a(7)=120 because the first six terms in the 7th row of Pascal's triangle 
               1+7+21+35+35+21=120 [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Jan 19 2009]
%p A006261 A006261:=(z**2-z+1)*(3*z**2-3*z+1)/(z-1)**6; [S. Plouffe in his 1992 
               dissertation.]
%o A006261 (Other) sage: [binomial(n,1)+binomial(n,3)+binomial(n,5) for n in xrange(1, 
               38)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 
               2009]
%Y A006261 A057703(n) + 1.
%Y A006261 A005408, A000124, A016813, A086514, A000125, A058331, A002522, A161701, 
               A161702, A161703, A000127, A161704, A161706, A161707, A161708, A161710, 
               A080856, A161711, A161712, A161713, A161715. [From Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Jun 17 2009]
%Y A006261 Sequence in context: A054043 A052396 A051040 this_sequence A145112 A062259 
               A001949
%Y A006261 Adjacent sequences: A006258 A006259 A006260 this_sequence A006262 A006263 
               A006264
%K A006261 nonn,easy
%O A006261 0,2
%A A006261 N. J. A. Sloane (njas(AT)research.att.com).

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