OFFSET
0,8
COMMENTS
Shifts 6 places left under 2nd-order binomial transform.
FORMULA
a(0) = ... = a(5) = 1; a(n) = Sum_{k=0..n-6} binomial(n-6,k) * 2^k * a(n-k-6).
MATHEMATICA
nmax = 31; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 A[x/(1 - 2 x)]/(1 - 2 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = If[n < 6, 1, Sum[Binomial[n - 6, k] 2^k a[n - k - 6], {k, 0, n - 6}]]; Table[a[n], {n, 0, 31}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 08 2022
STATUS
approved