Search: id:A000710
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%I A000710 M1375 N0535
%S A000710 1,2,5,10,20,35,62,102,167,262,407,614,919,1345,1952,2788,3950,5524,
%T A000710 7671,10540,14388,19470,26190,34968,46439,61275,80455,105047,136541,
%U A000710 176593,227460,291673,372605,474085,601105,759380,956249,1200143
%N A000710 Number of partitions of n, with two kinds of 1,2,3 and 4.
%C A000710 Also number of partitions of 2*n+4 with exactly 4 odd parts. - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Jan 12 2005
%D A000710 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000710 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000710 H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, 
               Vol. 4, Cambridge Univ. Press, 1958, p. 90.
%D A000710 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199.
%H A000710 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A000710 Euler transform of 2 2 2 2 1 1 1...
%F A000710 G.f.=1/[(1-x)(1-x^2)(1-x^3)(1-x^4)*product((1-x^k), k=1..infinity)].
%F A000710 a(n)=sum(A000098(n-4*j), j=0..floor(n/4)), n>=0.
%e A000710 a(2)=5 because we have 2, 2', 1+1, 1+1', 1+1'.
%p A000710 with (numtheory): etr:= proc(p) local b; b:=proc(n) option remember; 
               local d,j; if n=0 then 1 else add (add (d*p(d), d=divisors(j)) *b(n-j), 
               j=1..n)/n fi end end: a:= etr (n-> `if`(n<5,2,1)): seq (a(n), n=0..37); 
               [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008]
%Y A000710 Cf. A000712.
%Y A000710 Cf. A000070, A008951, A000097, A000098.
%Y A000710 Fifth column of Riordan triangle A008951 and of triangle A103923.
%Y A000710 Sequence in context: A039690 A126105 A117486 this_sequence A117487 A103924 
               A160647
%Y A000710 Adjacent sequences: A000707 A000708 A000709 this_sequence A000711 A000712 
               A000713
%K A000710 nonn,easy
%O A000710 0,2
%A A000710 N. J. A. Sloane (njas(AT)research.att.com).
%E A000710 Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 22 2005

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