OFFSET
2,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (21,-84,64).
FORMULA
a(n) = 4*A006105(n).
From Colin Barker, Aug 15 2014: (Start)
a(n) = (4-5*4^n+16^n)/45.
a(n) = 21*a(n-1)-84*a(n-2)+64*a(n-3).
G.f.: -4*x^2 / ((x-1)*(4*x-1)*(16*x-1)). (End)
MATHEMATICA
f[k_] := 4^(k - 1); t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 32}] (* A203244 *)
Table[a[n]/4, {n, 2, 32}] (* A006105 *)
LinearRecurrence[{21, -84, 64}, {4, 84, 1428}, 20] (* Harvey P. Dale, Aug 12 2015 *)
PROG
(PARI) Vec(-4*x^2/((x-1)*(4*x-1)*(16*x-1)) + O(x^100)) \\ Colin Barker, Aug 15 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 31 2011
EXTENSIONS
Typo in formula fixed by Colin Barker, Aug 15 2014
STATUS
approved