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A095871 Triangle read by rows: T(n,k)=(n+1)*(3*(n+1)-1)/2-k*(3*k-1)/2.

%I A095871 #15 Jun 17 2025 22:31:50
%S A095871 1,5,4,12,11,7,22,21,17,10,35,34,30,23,13,51,50,46,39,29,16,70,69,65,
%T A095871 58,48,35,19,92,91,87,80,70,57,41,22,117,116,112,105,95,82,66,47,25,
%U A095871 145,144,140,133,123,110,94,75,53,28,176,175,171,164,154,141,125,106,84,59
%N A095871 Triangle read by rows: T(n,k)=(n+1)*(3*(n+1)-1)/2-k*(3*k-1)/2.
%C A095871 Octagonal pyramidal number triangle, read by rows.
%C A095871 The triangle is generated from the product B*A of the infinite lower triangular matrices A =
%C A095871   1 0 0 0...
%C A095871   1 1 0 0...
%C A095871   1 1 1 0...
%C A095871   1 1 1 1...
%C A095871 and B =
%C A095871   1 0 0 0...
%C A095871   1 4 0 0...
%C A095871   1 4 7 0...
%C A095871   1 4 7 10...
%C A095871 T(n,0)=A000326(n+1)
%C A095871 T(n,2)=A059845(n+2)
%C A095871 T(n,n)=3*n+1
%F A095871 Triangle read by rows, T(n,k) = sum {j=k..n} 3*j - 2 = A000012 * ((3*j - 2) * 0^(n-k)) * A000012; 1<=k<=n. E.g. T(5,3) = 30 = (7 + 10 + 13).
%e A095871 Column 3 = A059845: 7, 17, 30, 46, 65...; while rightmost terms of rows are 1, 4, 7, 10...
%e A095871 First few rows of the triangle =
%e A095871   1;
%e A095871   5, 4;
%e A095871   12, 11, 7;
%e A095871   22, 21, 17, 10;
%e A095871   35, 34, 30, 23, 13;
%e A095871   51, 50, 46, 39, 29, 16;
%e A095871   70, 69, 65, 58, 48, 35, 19;
%e A095871   ...
%o A095871 (PARI) T(n, k) = local(i); if(k>n,0,(n+1)*(3*(n+1)-1)/2-k*(3*k-1)/2)
%o A095871 for(i=0,10, for(j=0,i,print1(T(i,j),", "));print()) \\ Lambert Klasen
%Y A095871 Cf. A095872, A000326, A059845, A002414 (row sums)
%K A095871 nonn,tabl
%O A095871 1,2
%A A095871 _Gary W. Adamson_, Jun 10 2004, Jul 28 2008
%E A095871 More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jan 21 2005