A351343
G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 * A(x/(1 - 2*x)) / (1 - 2*x).
Original entry on oeis.org
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
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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}]
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).
Original entry on oeis.org
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
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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}]
A351345
G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 * A(x/(1 - 2*x)) / (1 - 2*x).
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 1, 3, 9, 27, 81, 243, 729, 2189, 6601, 20141, 63009, 205989, 718905, 2720543, 11183601, 49321367, 228895201, 1097860903, 5371546897, 26598018425, 132755261681, 667027581401, 3376011676481, 17249045903945, 89270689572497, 470069622480667
Offset: 0
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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}]
Showing 1-3 of 3 results.
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