Search: id:A004126
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%I A004126
%S A004126 0,1,9,31,74,145,251,399,596,849,1165,1551,2014,2561,3199,3935,
%T A004126 4776,5729,6801,7999,9330,10801,12419,14191,16124,18225,20501,22959,
%U A004126 25606,28449,31495,34751,38224,41921,45849,50015,54426,59089,64011
%N A004126 n*(7*n^2-1)/6.
%C A004126 3-dimensional analogue of centered polygonal numbers.
%C A004126 Sum of n triangular numbers starting from T(n). E.g. a(4)= T(4) +T(5) 
               +T(6) +T(7) = 10+15+21+28 = 74. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), 
               Jul 16 2004
%C A004126 Also as a(n)=(1/6)*(7*n^3-n), n>0: structured heptagonal diamond numbers 
               (vertex structure 8) (Cf. A100179 = alternate vertex; A000447 = structured 
               diamonds; A100145 for more on structured numbers). - James A. Record 
               (james.record(AT)gmail.com), Nov. 7, 2004.
%C A004126 a(n)=A000447-A000292 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 21 2007
%D A004126 T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. 
               (11).
%F A004126 Partial sums of A069099, centered heptagonal numbers (A000566). - Jonathan 
               Vos Post (jvospost3(AT)gmail.com), Mar 16 2006
%F A004126 a(n)=C(2*n+1,3)-C(n+1,3), n>=0 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 21 2007
%p A004126 seq(binomial(2*n+1,3)-binomial(n+1,3), n=0..38); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 21 2007
%p A004126 a:=n->sum((n+j)^2-(n+j), j=1..n): seq(a(n)/2, n=0..38); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), May 26 2008
%Y A004126 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 A004126 Cf. A000217, A000566, A016993, A069099.
%Y A004126 Cf. A000447, A000292.
%Y A004126 Sequence in context: A054310 A072887 A133739 this_sequence A118444 A048374 
               A140323
%Y A004126 Adjacent sequences: A004123 A004124 A004125 this_sequence A004127 A004128 
               A004129
%K A004126 nonn
%O A004126 0,3
%A A004126 Albert D. Rich (Albert_Rich(AT)msn.com).

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