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A351343
G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 * A(x/(1 - 2*x)) / (1 - 2*x).
3
1, 1, 1, 1, 1, 3, 9, 27, 81, 245, 761, 2493, 8849, 34519, 147057, 670327, 3198561, 15732905, 79174929, 407127897, 2145061729, 11635963499, 65309080185, 380583443187, 2304629301041, 14475031232285, 93943897651017, 627220447621973, 4290783719133041, 29988917377046207
OFFSET
0,6
COMMENTS
Shifts 4 places left under 2nd-order binomial transform.
FORMULA
a(0) = ... = a(3) = 1; a(n) = Sum_{k=0..n-4} binomial(n-4,k) * 2^k * a(n-k-4).
MATHEMATICA
nmax = 29; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 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 < 4, 1, Sum[Binomial[n - 4, k] 2^k a[n - k - 4], {k, 0, n - 4}]]; Table[a[n], {n, 0, 29}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 08 2022
STATUS
approved