Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
reviewed
approved
proposed
reviewed
editing
proposed
<a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,153,0,0,0,-153,0,0,0,1).
Conjectures from _From _Colin Barker_, Nov 03 2020: (Start)
a(n) = 153*a(n-4) - 153*a(n-8) + a(n-12) for n>1112.
proposed
editing
editing
proposed
Conjectures from Colin Barker, Nov 03 2020: (Start)
G.f.: x*(1 + x + x^2 + x^3 - 152*x^4 - 147*x^5 - 137*x^6 - 112*x^7 + 106*x^8 + 41*x^9 + 16*x^10 + 6*x^11) / ((1 - x)*(1 + x)*(1 + x^2)*(1 - 152*x^4 + x^8)).
a(n) = 153*a(n-4) - 153*a(n-8) + a(n-12) for n>11.
(End)
proposed
editing
editing
proposed
a[n_] := a[n] = If[n <= 5, 1, SwitchWith[{m = If[Mod[n, 4], == 2, 8, 3]}, m a[n-1] - a[n-2] - 1]];
0, 3 a[n - 1] - a[n - 2] - 1,
1, 3 a[n - 1] - a[n - 2] - 1,
2, 8 a[n - 1] - a[n - 2] - 1,
3, 3 a[n - 1] - a[n - 2] - 1]];
proposed
editing
editing
proposed
a[n_] := a[n] = If[n <= 5, 1, Switch[Mod[n, 4],
0, 3 a[n - 1] - a[n - 2] - 1,
1, 3 a[n - 1] - a[n - 2] - 1,
2, 8 a[n - 1] - a[n - 2] - 1,
3, 3 a[n - 1] - a[n - 2] - 1]];
Array[a, 30] (* Jean-François Alcover, Nov 03 2020 *)
approved
editing