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A351344
G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 * A(x/(1 - 2*x)) / (1 - 2*x).
3
1, 1, 1, 1, 1, 1, 3, 9, 27, 81, 243, 731, 2223, 6939, 22727, 79971, 306929, 1282815, 5744361, 26984415, 130656409, 644739377, 3224303841, 16318576681, 83717193681, 436948772697, 2331807007139, 12791837178265, 72472130039123, 425239734375217, 2584950704996379
OFFSET
0,7
COMMENTS
Shifts 5 places left under 2nd-order binomial transform.
FORMULA
a(0) = ... = a(4) = 1; a(n) = Sum_{k=0..n-5} binomial(n-5,k) * 2^k * a(n-k-5).
MATHEMATICA
nmax = 30; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 + x^5 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 < 5, 1, Sum[Binomial[n - 5, k] 2^k a[n - k - 5], {k, 0, n - 5}]]; Table[a[n], {n, 0, 30}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 08 2022
STATUS
approved