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 A276382 #38 Sep 09 2023 10:06:47
%S A276382 1,5,10,17,25,35,46,59,73,89,106,125,145,167,190,215,241,269,298,329,
%T A276382 361,395,430,467,505,545,586,629,673,719,766,815,865,917,970,1025,
%U A276382 1081,1139,1198,1259,1321,1385,1450,1517,1585,1655,1726,1799,1873,1949,2026
%N A276382 a(1) = 1, and a(n) = a(n-1) + floor(3*n/2) + 1 for n >= 2.
%C A276382 Given 3 distinct numbers i, j and k whose prime signatures are exactly n 1's, then a(n) is the number of prime signatures for all permutations of i*j*k.
%C A276382 a(n) is the number of partitions of 3n such that there are no more than n-1 3's and no parts > 3.
%C A276382 a(3n+1) represents the number of prime signature sets whose members are excluded as terms in A026477, as a consequence of being products of three smaller terms whose prime signatures are exactly 3n+1 1's.
%C A276382 First differences are floor(3n/2) + 1 (A001651(n+1)); second differences are 1 when n is even and 2 when n is odd; third differences are 1 when n is even and -1 when n is odd.
%H A276382 Colin Barker, <a href="/A276382/b276382.txt">Table of n, a(n) for n = 1..1000</a>
%H A276382 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A276382 From _Colin Barker_, Sep 01 2016: (Start)
%F A276382 a(n) = ((-1)^n + 12*n + 6*n^2 - 9)/8 for n > 0.
%F A276382 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n > 4.
%F A276382 G.f.: x*(1 + 3*x - x^3) / ((1-x)^3*(1+x)). (End)
%F A276382 a(n) = -1 + Sum_{k=1..n} floor((n+k+3)/2). - _Wesley Ivan Hurt_, Apr 01 2017
%F A276382 a(n) = a(-2-n) for all n in Z. - _Michael Somos_, Sep 08 2023
%F A276382 a(n) = floor((3*(n+1)^2 - 7)/4). - _Michael Somos_, Sep 09 2023
%e A276382 a(2)=5; the 5 prime signatures / partitions are: {3,1,1,1}, {2,2,2}, {2,2,1,1}, {2,1,1,1} and {1,1,1,1,1,1}.
%e A276382 G.f. = x + 5*x^2 + 10*x^3 + 17*x^4 + 25*x^5 + 35*x^6 + 46*x^7 + ... - _Michael Somos_, Sep 08 2023
%t A276382 a[1] = 1; a[n_] := a[n] = a[n - 1] + Floor[3 n/2] + 1 ; Array[a, 51] (* _Michael De Vlieger_, Sep 01 2016 *)
%t A276382 a[n_] := Floor[(3*(n+1)^2 - 7)/4]; (* _Michael Somos_, Sep 08 2023 *)
%o A276382 (PARI) Vec(x*(1+3*x-x^3)/((1-x)^3*(1+x)) + O(x^60)) \\ _Colin Barker_, Sep 01 2016
%o A276382 (PARI) {a(n) = (3*(n+1)^2 - 7)\4}; /* _Michael Somos_, Sep 09 2023 */
%o A276382 (Magma) [((-1)^n+12*n+6*n^2-9)/8: n in [1..60]]; // _Vincenzo Librandi_, Sep 10 2016
%Y A276382 Cf. A000040 (prime numbers), A001651, A026477.
%Y A276382 Equals one less than A331952(n+1), two less than A077043(n+1), and three less than A084684(n+1). - _Greg Dresden_, Feb 22 2020
%K A276382 nonn,easy
%O A276382 1,2
%A A276382 _Bob Selcoe_, Sep 01 2016