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 A332410 #32 Apr 24 2020 18:55:05
%S A332410 0,1,3,6,11,17,24,32,41,52,64,77,91,106,123,141,160,180,201,224,248,
%T A332410 273,299,326,355,385,416,448,481,516,552,589,627,666,707,749,792,836,
%U A332410 881,928,976,1025,1075,1126,1179
%N A332410 a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7) with a(0)=0, a(1)=1, a(2)=3, a(3)=6, a(4)=11, a(5)=17, a(6)=24.
%C A332410 This sequence occurs twice as a linear spoke in the hexagonal spiral constructed from A002266:
%C A332410 17 17 17 17 17 18 18
%C A332410 16 11 11 11 11 12 12 18
%C A332410 16 11 6 6 7 7 7 12 18
%C A332410 16 10 6 3 3 3 3 7 12 18
%C A332410 16 10 6 3 1 1 1 4 7 12 19
%C A332410 16 10 6 2 0 0 0 1 4 8 13 19
%C A332410 15 10 5 2 0 0 1 4 8 13 19
%C A332410 15 10 5 2 2 2 4 8 13 19
%C A332410 15 9 5 5 5 4 8 13 19
%C A332410 15 9 9 9 9 8 13 20
%C A332410 15 14 14 14 14 14 20
%C A332410 a(-1-n) = 0, 1, 4, 8, 13, 19, 26, 35, 45, ... also occurs twice in the same spiral.
%C A332410 Difference table:
%C A332410 0, 1, 3, 6, 11, 17, 24, 32, 41, 52, ... = a(n)
%C A332410 1, 2, 3, 5, 6, 7, 8, 9, 11, 12, ... = A047256(n+1)
%C A332410 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, ... = A130782.
%C A332410 There is no linear spoke with three copies in this spiral. Compare with the spiral illustrated in sequence A330707 and constructed from A002265 where the same spokes occur three times: A006578, A001859 and A077043, essentially. Strictly, three times from 1, 1, 1 for A006578, from 2, 2, 2 for A001859 and from 7, 7, 7 for A077043.
%H A332410 Colin Barker, <a href="/A332410/b332410.txt">Table of n, a(n) for n = 0..1000</a>
%H A332410 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1).
%F A332410 a(8+n) - a(8-n) = 20*n.
%F A332410 G.f.: x*(1 + x)*(1 + x^2 + x^3) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, Feb 11 2020
%t A332410 LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {0, 1, 3, 6, 11, 17, 24}, 45] (* _Amiram Eldar_, Feb 12 2020 *)
%o A332410 (PARI) concat(0, Vec(x*(1 + x)*(1 + x^2 + x^3) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)) + O(x^50))) \\ _Colin Barker_, Feb 11 2020, Apr 24 2020
%Y A332410 Cf. A002266, A008602, A047256, A130782, A330707.
%Y A332410 Cf. A001859, A006578, A077043.
%K A332410 nonn,easy
%O A332410 0,3
%A A332410 _Paul Curtz_, Feb 11 2020