A344491
a(n) = 1 + Sum_{k=0..n-4} binomial(n-3,k) * a(k).
Original entry on oeis.org
1, 1, 1, 1, 2, 4, 8, 16, 37, 97, 275, 810, 2468, 7840, 26182, 92047, 339029, 1299185, 5152244, 21091816, 89087652, 388318264, 1746324563, 8094422821, 38608318847, 189179752492, 950930369320, 4898477508796, 25841317224002, 139534769647745, 770795537345237, 4353368099507329
Offset: 0
-
a[n_] := a[n] = 1 + Sum[Binomial[n - 3, k] a[k] , {k, 0, n - 4}]; Table[a[n], {n, 0, 31}]
nmax = 31; A[] = 0; Do[A[x] = (1 + x^3 A[x/(1 - x)])/((1 - x) (1 + x^3)) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
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
-
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}]
A351707
G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 * A(x/(1 - x)) / (1 - x)^2.
Original entry on oeis.org
1, 1, 1, 1, 1, 3, 7, 15, 31, 65, 147, 373, 1051, 3157, 9761, 30573, 96965, 313999, 1049719, 3654303, 13284783, 50268837, 196638987, 789611161, 3238765671, 13540348965, 57710600953, 251163156089, 1118308871001, 5100825621147, 23838465463447, 114044805729151
Offset: 0
-
nmax = 31; A[] = 0; Do[A[x] = 1 + x + x^2 + x^3 + x^4 A[x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = If[n < 4, 1, Sum[Binomial[n - 3, k + 1] a[k], {k, 0, n - 4}]]; Table[a[n], {n, 0, 31}]
Showing 1-3 of 3 results.
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