Search: id:A101447
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%I A101447
%S A101447 1,2,3,3,6,5,4,9,10,7,5,12,15,14,9,6,15,20,21,18,11,7,18,25,28,27,22,13,
%T A101447 8,21,30,35,36,33,26,15,9,24,35,42,45,44,39,30,17,10,27,40,49,54,55,52,
%U A101447 45,34,19,11,30,45,56,63,66,65,60,51,38,21,12,33,50,63,72,77,78,75,68
%N A101447 Triangle read by rows: T(n,k) = (2*k+1)*(n+1-k), 0<=k<n.
%C A101447 The triangle is generated from the product of matrix A and matrix B, 
               I.e. A * B where A = the infinite lower triangular matrix:
%C A101447 1 0 0 0 0 ...
%C A101447 1 1 0 0 0 ...
%C A101447 1 1 1 0 0 ...
%C A101447 1 1 1 1 0 ...
%C A101447 1 1 1 1 1 ...
%C A101447 ... and B = the infinite lower triangular matrix:
%C A101447 1 0 0 0 0...
%C A101447 1 3 0 0 0...
%C A101447 1 3 5 0 0...
%C A101447 1 3 5 7 0...
%C A101447 1 3 5 7 9...
%C A101447 ...
%C A101447 Row sums give the square pyramidal numbers A000330.
%C A101447 T(n+0,0)=1*n=A000027(n+1); T(n+1,1)=3*n=A008585(n); T(n+2,2)=5*n=A008587(n); 
               T(n+3,3)=7*n=A008589(n); etc. So T(n,0)*T(n,1)=3*n*(n+1)=A028896(n) 
               (6 times triangular numbers.) T(n,1)*T(n,2)/10=3*n*(n+1)/2=A045943(n) 
               for n>0 T(n,2)*T(n,3)/10=7/2*n*(n+1)=A024966(n) for n>1 (7 times 
               triangular numbers.) etc.
%t A101447 t[n_, k_] := If[n < k, 0, (2*k + 1)*(n - k + 1)]; Flatten[ Table[ t[n, 
               k], {n, 0, 11}, {k, 0, n}]] (from Robert G. Wilson v Jan 20 2005)
%o A101447 (PARI) T(n,k)=if(n<k,0,(2*k+1)*(n-k+1)) for(i=0,15, for(j=0,i,print1(T(i,
               j),","));print())
%Y A101447 Cf. A094728 (triangle generated by B*A), A000330.
%Y A101447 Sequence in context: A160791 A115973 A057047 this_sequence A119322 A014498 
               A023821
%Y A101447 Adjacent sequences: A101444 A101445 A101446 this_sequence A101448 A101449 
               A101450
%K A101447 nonn,tabl
%O A101447 0,2
%A A101447 Lambert Klasen (lambert.klasen(AT)gmx.de) and Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Jan 19 2005

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