A330651 a(n) = n^4 + 3*n^3 + 2*n^2 - 2*n.

0, 4, 44, 174, 472, 1040, 2004, 3514, 5744, 8892, 13180, 18854, 26184, 35464, 47012, 61170, 78304, 98804, 123084, 151582, 184760, 223104, 267124, 317354, 374352, 438700, 511004, 591894, 682024, 782072, 892740, 1014754, 1148864, 1295844

Offset: 0

Author

Ed Pegg Jr, Jan 15 2020

Keywords

• nonn
• easy

Comments

a(n)/A269657(n) gives unforgeable word approximations (A003000) with increasing accuracy, as follows: 4/15, 44/79, 174/253, ... ~ 0.26 (A242430), 0.5569 (A019308), 0.68774 (A019309), 0.8055770, 0.83674321, 0.85937882, 0.87654509, 0.89000100, 0.9008270111, ....

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A269657, A242430, A003000, A019308, A019309.

Programs

Maple

A330651 := n -> (((n+3)*n+2)*n-2)*n; # M. F. Hasler, Feb 29 2020

Mathematica

Numerator/@Table[(-2 n+2 n^2+3 n^3+n^4)/(1+3 n+6 n^2+4 n^3+n^4),{n,0,33}] (* Ed Pegg Jr, Jan 15 2020 *)

PARI

Vec(2*x*(2 + 12*x - 3*x^2 + x^3) / (1 - x)^5 + O(x^40),-40) \\ Colin Barker, Jan 15 2020

PARI

apply( {A330651(n)=(((n+3)*n+2)*n-2)*n}, [0..44]) \\ M. F. Hasler, Feb 29 2020

Formula

From Colin Barker, Jan 15 2020: (Start)

G.f.: 2*x*(2 + 12*x - 3*x^2 + x^3) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

E.g.f.: exp(x)*x*(4 + 18*x + 9*x^2 + x^3). - Stefano Spezia, Feb 03 2020