Search: id:A001402
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%I A001402 M0662 N0243
%S A001402 1,1,2,3,5,7,11,14,20,26,35,44,58,71,90,110,136,163,199,235,282,331,
%T A001402 391,454,532,612,709,811,931,1057,1206,1360,1540,1729,1945,2172,2432,
%U A001402 2702,3009,3331,3692,4070,4494,4935,5427,5942,6510,7104,7760,8442,9192
%N A001402 Number of partitions of n into at most 6 parts.
%D A001402 A. Cayley, Calculation of the minimum N.G.F. of the binary seventhic, 
               Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, 
               London, 1889-1897, Vol. 10, p. 408-419.
%D A001402 H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, 
               Vol. 4, Cambridge Univ. Press, 1958, p. 2.
%D A001402 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001402 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001402 T. D. Noe, <a href="b001402.txt">Table of n, a(n) for n=0..1000</a>
%H A001402 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=355">
               Encyclopedia of Combinatorial Structures 355</a>
%F A001402 a(n)=1+(a(n-2)+a(n-3)+a(n-4))-(2*a(n-7)+2*a(n-8)+a(n-9))+(a(n-11)+2*a(n-12)+2*a(n-13))- 
               (a(n-16)+a(n-17)+a(n-18))+(a(n-20)) - Norman J. Meluch (norm(AT)iss.gm.com), 
               Mar 09 2000
%p A001402 with(combstruct):ZL7:=[S,{S=Set(Cycle(Z,card<7))}, unlabeled]: seq(count(ZL7,
               size=n),n=0..50); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Sep 24 2007
%p A001402 (Maple) a := n -> (Matrix(21, (i,j)-> if (i=j-1) then 1 elif j=1 then 
               [1, 1, 0, 0, -1, 0, -2, 0, 1, 1, 1, 1, 0, -2, 0, -1, 0, 0, 1, 1, 
               -1][i] else 0 fi)^n)[1,1]; seq (a(n), n=0..50); [From Alois P. Heinz 
               (heinz(AT)hs-heilbronn.de), Jul 31 2008]
%p A001402 B:=[S,{S = Set(Sequence(Z,1 <= card),card <=6)},unlabelled]: seq(combstruct[count](B, 
               size=n), n=0..50);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 21 2009]
%t A001402 CoefficientList[ Series[ 1/((1 - x)*(1 - x^2)*(1 - x^3)*(1 - x^4)*(1 
               - x^5)*(1 - x^6)), {x, 0, 60} ], x ]
%Y A001402 Essentially same as A026812.
%Y A001402 a(n)=A008284(n+6, 6), n >= 0.
%Y A001402 Sequence in context: A036608 A136185 A026812 this_sequence A008629 A070289 
               A035961
%Y A001402 Adjacent sequences: A001399 A001400 A001401 this_sequence A001403 A001404 
               A001405
%K A001402 nonn,easy
%O A001402 0,3
%A A001402 N. J. A. Sloane (njas(AT)research.att.com).

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