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 A104394 #14 Feb 16 2025 08:32:56 %S A104394 56,91,111,121,125,147,167,177,181,202,212,216,231,232,236,246,251, %T A104394 261,265,286,296,300,316,320,330,342,351,352,356,371,372,376,381,385, %U A104394 386,406,407,411,416,420,421,436,440,441,450,462,472,476,492,496 %N A104394 Sums of 4 distinct positive pentatope numbers (A000332). %C A104394 Pentatope number Ptop(n) = binomial(n+3,4) = n*(n+1)*(n+2)*(n+3)/24. Hyun Kwang Kim asserts that every positive integer can be represented as the sum of no more than 8 pentatope numbers; but in this sequence we are only concerned with sums of nonzero distinct pentatope numbers. %D A104394 Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 55-57, 1996. %H A104394 Hyun Kwang Kim, <a href="http://dx.doi.org/10.1090/S0002-9939-02-06710-2">On Regular Polytope Numbers</a>, Proc. Amer. Math. Soc., 131 (2003), 65-75. %H A104394 J. V. Post, <a href="http://www.magicdragon.com/poly.html">Table of Polytope Numbers, Sorted, Through 1,000,000</a>. %H A104394 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentatopeNumber.html">Pentatope Number</a>. %F A104394 a(n) = Ptop(h) + Ptop(i) + Ptop(j) + Ptop(k) for some positive h=/=i=/=j=/=k and Ptop(n) = binomial(n+3,4). %Y A104394 Cf. A000332, A100009, A102857, A104392, A104393. %K A104394 easy,nonn %O A104394 1,1 %A A104394 _Jonathan Vos Post_, Mar 05 2005 %E A104394 Extended by _Ray Chandler_, Mar 05 2005