This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A101493 #16 Mar 07 2019 21:53:02 %S A101493 1,6,5,15,14,9,28,27,22,13,45,44,39,30,17,66,65,60,51,38,21,91,90,85, %T A101493 76,63,46,25,120,119,114,105,92,75,54,29,153,152,147,138,125,108,87, %U A101493 62,33,190,189,184,175,162,145,124,99,70,37,231,230,225,216,203,186,165,140,111,78,41 %N A101493 Triangle read by rows: T(n,k) = (n+1)*(2*(n+1)-1) - k*(2*k-1). %C A101493 The triangle is generated from the product B*A of the infinite lower triangular matrices A = %C A101493 1 0 0 0 ... %C A101493 1 1 0 0 ... %C A101493 1 1 1 0 ... %C A101493 1 1 1 1 ... %C A101493 ... and B = %C A101493 1 0 0 0 ... %C A101493 1 5 0 0 ... %C A101493 1 5 9 0 ... %C A101493 1 5 9 13 ... %C A101493 ... %C A101493 T(n+0,0) = n*(2*n-1) = A000384(n) (Hexagonal numbers) %C A101493 since T(n,n) = 4*n+1 = A016813(n). %C A101493 T(n,n) = 4*n + 1 = A016813(n); %C A101493 T(n+1,n) = 8*n + 6 = A017137(n); %C A101493 T(n+2,n) = 12*n + 3 = A017557(n); %C A101493 T(n,n)*T(n,0) = (n+1)*(2*n+1)*(4*n+1) = A079588(n). %H A101493 Muniru A Asiru, <a href="/A101493/b101493.txt">Rows n = 0..150 of triangle, flattened</a> %e A101493 Triangle begins: %e A101493 1; %e A101493 6, 5; %e A101493 15, 14, 9; %e A101493 28, 27, 22, 13; %e A101493 45, 44, 39, 30, 17; %e A101493 66, 65, 60, 51, 38, 21; %o A101493 (PARI) T(n,k)=if(k>n,0,(n+1)*(2*(n+1)-1)-k*(2*k-1)) %o A101493 for(i=0,10, for(j=0,i,print1(T(i,j),", "));print()) %o A101493 (GAP) Flat(List([0..10],n->List([0..n],k->(n+1)*(2*n+1)-k*(2*k-1)))); # _Muniru A Asiru_, Mar 05 2019 %Y A101493 Row sums give 10-gonal pyramidal numbers: n(n+1)(8n-5)/6 = A007585(n+1). %Y A101493 Cf. A101492 (for product A*B), A007585, A000384. %K A101493 nonn,tabl %O A101493 0,2 %A A101493 Lambert Klasen (lambert.klasen(AT)gmx.de) and _Gary W. Adamson_, Jan 21 2005