A307469 a(n) = 2*a(n-1) + 6*a(n-2) for n >= 2, a(0) = 1, a(1) = 5.
1, 5, 16, 62, 220, 812, 2944, 10760, 39184, 142928, 520960, 1899488, 6924736, 25246400, 92041216, 335560832, 1223368960, 4460102912, 16260419584, 59281456640, 216125430784, 787939601408, 2872631787520, 10472901183488, 38181593092096, 139200593285120
Offset: 0
Examples
For n=2 the a(2)=16 solutions are: 12, 14, 21, 22, 23, 24, 25, 32, 34, 41, 42, 43, 44, 45, 52, 54.
Links
- Index entries for linear recurrences with constant coefficients, signature (2,6).
Crossrefs
The same over alphabet {1,2,3} gives A001045(n+2).
Programs
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Maple
aseq:=proc(n) option remember; if n<0 then return "seq not defined for negative indices"; elif n=0 then return 1; elif n=1 then return 5; else 2*aseq(n-1)+6*aseq(n-2); end if; end proc: seq(aseq(n),n=0..26);
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Mathematica
a[0] = 1; a[1] = 5; a[n_] := a[n] = 2*a[n - 1] + 6*a[n - 2]; Table[a[n], {n, 0, 26}] LinearRecurrence[{2,6},{1,5},30] (* Harvey P. Dale, Feb 20 2023 *)
Formula
a(n) = (-(2/7)*sqrt(7)+1/2)*(1-sqrt(7))^n+((2/7)*sqrt(7)+1/2)*(1+sqrt(7))^n.
G.f.: (1+3*x)/(1-2*x-6*x^2).
Comments