A111607 Fourth column of A109626.

1, 2, 3, 3, 5, 3, 7, 2, 9, 10, 11, 9, 13, 7, 15, 4, 17, 18, 19, 15, 21, 11, 23, 6, 25, 26, 27, 21, 29, 15, 31, 8, 33, 34, 35, 27, 37, 19, 39, 10, 41, 42, 43, 33, 45, 23, 47, 12, 49, 50, 51, 39, 53, 27, 55, 14, 57, 58, 59, 45, 61, 31, 63, 16, 65, 66, 67, 51, 69, 35, 71, 18, 73, 74, 75

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

G.f.: x*(1 + 2*x + 3*x^2 + 3*x^3 + 5*x^4 + 3*x^5 + 7*x^6 + 2*x^7 + 7*x^8 + 6*x^9 + 5*x^10 + 3*x^11 + 3*x^12 + x^13 + x^14)/(1-x^8)^2.

Mathematica

(* First program *)
f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[a[j], {j, 0, 128}]]; g[n_, m_] := f[n][[m]]; Table[g[n, 4 + 1], {n, 75}]
(* Alternative: *)
CoefficientList[Series[(1+2*x+3*x^2+3*x^3+5*x^4+3*x^5+7*x^6+2*x^7+7*x^8 +6*x^9+5*x^10+3*x^11+3*x^12+x^13+x^14)/(1-x^8)^2, {x, 0, 100}], x] (* G. C. Greubel, Jan 29 2025 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 102);
p:= func< x | x*(1+2*x+3*x^2+3*x^3 +5*x^4 +3*x^5 +7*x^6 +2*x^7 +7*x^8 +6*x^9 +5*x^10 +3*x^11 +3*x^12 +x^13 +x^14)/(1-x^8)^2 >;
Coefficients(R!( p(x) )); // G. C. Greubel, Jan 29 2025
(SageMath)
def p(x): return x*(1+2*x+3*x^2+3*x^3 +5*x^4 +3*x^5 +7*x^6 +2*x^7 +7*x^8 +6*x^9 +5*x^10 +3*x^11 +3*x^12 +x^13 +x^14)
def A111607_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( p(x)/(1-x^8)^2 ).list()
a=A111607_list(101); a[1:] # G. C. Greubel, Jan 29 2025

Crossrefs

Cf. A109626.

Sequence in context: A140187 A214127 A381934 * A327124 A329277 A117531

Adjacent sequences: A111604 A111605 A111606 * A111608 A111609 A111610

Keyword

nonn

Author

Paul D. Hanna and Robert G. Wilson v, Aug 01 2005

Status

approved