Search: id:A004188
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%I A004188
%S A004188 0,1,11,39,94,185,321,511,764,1089,1495,1991,2586,3289,4109,5055,
%T A004188 6136,7361,8739,10279,11990,13881,15961,18239,20724,23425,26351,
%U A004188 29511,32914,36569,40485,44671,49136,53889,58939,64295,69966,75961
%N A004188 n*(3*n^2-1)/2.
%C A004188 3-dimensional analogue of centered polygonal numbers.
%C A004188 (1), (4+7), (10+13+16), (19+22+25+28), ... - Jon Perry (perry(AT)globalnet.co.uk), 
               Sep 10 2004
%C A004188 a(n)=A000447+A000292 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 21 2007
%D A004188 T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. 
               (11).
%F A004188 Partial sums of n-1 3-spaced triangular numbers, e.g. a(4)=t(1)+t(4)+t(7)=1+10+28=39 
               - Jon Perry (perry(AT)globalnet.co.uk), Jul 23 2003
%F A004188 a(n)=C(2*n+1,3)+C(n+1,3), n>=0 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 21 2007
%p A004188 seq(binomial(2*n+1,3)+binomial(n+1,3), n=0..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 21 2007
%o A004188 (PARI) v=vector(40,i,t(i)); s=0; forstep(i=1,40,3,s+=v[i]; print1(s",
               "))
%Y A004188 1/12*t*(n^3-n)+n for t = 2, 4, 6, ... gives A004006, A006527, A006003, 
               A005900, A004068, A000578, A004126, A000447, A004188, A004466, A004467, 
               A007588, A062025, A063521, A063522, A063523.
%Y A004188 Cf. A016061, A002412.
%Y A004188 Cf. A051682.
%Y A004188 Sequence in context: A103738 A045801 A162261 this_sequence A163634 A127867 
               A138050
%Y A004188 Adjacent sequences: A004185 A004186 A004187 this_sequence A004189 A004190 
               A004191
%K A004188 nonn
%O A004188 0,3
%A A004188 Albert D. Rich (Albert_Rich(AT)msn.com).

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