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 A103217 #15 Feb 16 2025 08:32:56
%S A103217 1,6,1,15,6,1,28,15,6,1,45,28,15,6,1,66,45,28,15,6,1,91,66,45,28,15,6,
%T A103217 1,120,91,66,45,28,15,6,1,153,120,91,66,45,28,15,6,1,190,153,120,91,
%U A103217 66,45,28,15,6,1,231,190,153,120,91,66,45,28,15,6,1,276,231,190,153,120,91,66
%N A103217 Hexagonal numbers triangle read by rows: T(n,k)=(n+1-k)*(2*(n+1-k)-1).
%C A103217 The triangle is generated by the product A*B = B*A of the infinite lower triangular matrices A =
%C A103217 1 0 0 0...
%C A103217 1 1 0 0...
%C A103217 1 1 1 0...
%C A103217 1 1 1 1...
%C A103217 ...
%C A103217 and B =
%C A103217 1 0 0 0...
%C A103217 5 1 0 0...
%C A103217 9 5 1 0...
%C A103217 13 9 5 1...
%C A103217 ...
%C A103217 The only prime hexagonal pyramidal number is 7. The only semiprime hexagonal pyramidal numbers are: 22, 95, 161. All greater hexagonal pyramidal numbers A002412 have at least 3 prime factors. Note that 7337 = 11 * 23 * 29 is a palindromic 3-brilliant number and 65941 = 23 * 47 * 61 is 3-brilliant. - _Jonathan Vos Post_, Jan 26 2005
%H A103217 Jonathan Vos Post, <a href="https://web.archive.org/web/20200219170305/http://www.magicdragon.com:80/poly.html">Table of Polytope Numbers, Sorted, Through 1,000,000</a>.
%H A103217 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HexagonalNumber.html">Hexagonal Number</a>.
%H A103217 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HexagonalPyramidalNumber.html">Hexagonal Pyramidal Number</a>.
%e A103217 Triangle begins:
%e A103217 1,
%e A103217 6,1,
%e A103217 15,6,1,
%e A103217 28,15,6,1,
%e A103217 45,28,15,6,1,
%e A103217 66,45,28,15,6,1,
%e A103217 91,66,45,28,15,6,1,
%t A103217 T[n_, k_] := (n + 1 - k)*(2*(n + 1 - k) - 1); Flatten[ Table[ T[n, k], {n, 0, 10}, {k, 0, n}]] (* _Robert G. Wilson v_, Feb 10 2005 *)
%o A103217 (PARI) T(n, k) = (n+1-k)*(2*(n+1-k)-1); for(i=0,10, for(j=0,i,print1(T(i,j),",")); print())
%Y A103217 Row sums give A002412 (hexagonal pyramidal numbers).
%Y A103217 Cf. A000384, A002412.
%K A103217 easy,nonn,tabl
%O A103217 0,2
%A A103217 Lambert Klasen (lambert.klasen(AT)gmx.de) and _Gary W. Adamson_, Jan 25 2005