Search: id:A094414
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%I A094414
%S A094414 1,5,4,14,11,11,30,24,22,24,55,45,40,40,45,91,76,67,64,67,76,140,119,
%T A094414 105,98,98,105,119,204,176,156,144,140,144,156,176,285,249,222,204,195,
%U A094414 195,204,222,249,385,340,305,280,265,260,265,280,305,340,506,451
%N A094414 Triangle T read by rows: dot product <1,2,...,r> * <s+1,s+2,...,r,1,2,
               ...,s>.
%C A094414 Offset for r (the rows) is 1, for s (the columns) it is 0.
%F A094414 T(r, s) = r(2r^2 + 3r - 3rs + 1 + 3s^2)/6, r>=1, 0<=s<=r-1.
%e A094414 1
%e A094414 5 4
%e A094414 14 11 11
%e A094414 30 24 22 24
%e A094414 55 45 40 40 45
%e A094414 91 76 67 64 67 76
%p A094414 T:=proc(r,s) if s>=r then 0 else r*(2*r^2+3*r+1-3*r*s+3*s^2)/6 fi end: 
               for r from 1 to 11 do seq(T(r,s),s=0..r-1) od; # yields sequence 
               in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 
               27 2006
%Y A094414 Columns 0-6 are A000330, A006527, A026037, A026040, A026043, A026046, 
               A026049. Row sums are A000537. See also A094415, A088003.
%Y A094414 Sequence in context: A019068 A147685 A078930 this_sequence A158867 A107984 
               A133178
%Y A094414 Adjacent sequences: A094411 A094412 A094413 this_sequence A094415 A094416 
               A094417
%K A094414 nonn,tabl
%O A094414 0,2
%A A094414 Ralf Stephan, May 02 2004

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