A086822 a(n) = floor((6*n^0+5*n^1+4*n^2+3*n^3) / (1*n^0+1*n^1+1*n^2)).

6, 8, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154, 157, 160, 163, 166, 169, 172, 175

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = floor(3n+1+(5+n)/(1+n+n^2)) = 3n+1 = A112414(n-2) for n>2. - R. J. Mathar, Dec 13 2008

a(n) = 2*a(n-1)-a(n-2) for n>4. - Colin Barker, May 23 2015

G.f.: x*(x^3-4*x+6) / (x-1)^2. - Colin Barker, May 23 2015

Example

a(3) = floor((6*3^0+5*3^1+4*3^2+3*3^3)/(1*3^0+1*3^1+1*3^2)) = floor(138/13) = floor(10.615) = 10.

Mathematica

Table[Floor[(6+5n+4n^2+3n^3)/(1+n+n^2)], {n, 60}] (* Harvey P. Dale, Apr 22 2018 *)

Prog

(PARI) Vec(x*(x^3-4*x+6)/(x-1)^2 + O(x^100)) \\ Colin Barker, May 23 2015

Crossrefs

Cf. A086790, A086814.

Sequence in context: A330976 A181764 A153032 * A048943 A255429 A319238

Adjacent sequences: A086819 A086820 A086821 * A086823 A086824 A086825

Keyword

easy,nonn

Author

Wang Dan (wangdan01(AT)lycos.com), Aug 07 2003

Status

approved