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 A145920 #22 Feb 16 2025 08:33:09 %S A145920 0,1,5,35,70,210,330,715,1001,1820,2380,3876,4845,7315,8855,12650, %T A145920 14950,20475,23751,31465,35960,46376,52360,66045,73815,91390,101270, %U A145920 123410,135751,163185,178365,211876,230300,270725,292825,341055,367290,424270 %N A145920 List of numbers that are both pentagonal (A000326) and binomial coefficients C(n,4) (A000332). %C A145920 All binomial coefficients C(n,4) belong to the generalized pentagonal sequence (A001318). %C A145920 Pentagonal numbers of generalized pentagonal number (A001318) index number. - _Raphie Frank_, Nov 25 2012 %H A145920 William A. Tedeschi, <a href="/A145920/b145920.txt">Table of n, a(n) for n = 1..10000</a> %H A145920 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>. %H A145920 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentatopeNumber.html">Pentatope Number</a>. %F A145920 a(n+1) = A000326 (A001318(n)). %F A145920 Positive values of A000332(n) belong to the sequence if and only if 3 does not divide n. A000332(n) is positive when n>3. %F A145920 Conjecture: a(n) = a(n-1) + 4a(n-2) - 4a(n-3) - 6a(n-4) + 6a(n-5) + 4a(n-6) - 4a(n-7) - a(n-8) + a(n-9). - _R. J. Mathar_, Oct 29 2008 %F A145920 Conjecture: G.f.: x^2(1 + 4x + 26x^2 + 19x^3 + 4x^5 + x^6 + 26x^4)/((1+x)^4(1-x)^5). - _R. J. Mathar_, Oct 29 2008 %F A145920 a(n) = (27x^4 - 18x^3 - 3x^2 + 2x)/8 where x = floor(n/2)*(-1)^n, for n >= 1. - _William A. Tedeschi_, Aug 16 2010 %e A145920 35, for example, is both A000326(5) and A000332(7). %Y A145920 Cf. A141919, of which this is a subsequence. %K A145920 easy,nonn %O A145920 1,3 %A A145920 _Matthew Vandermast_, Oct 28 2008