A028212 Expansion of 1/((1-6x)(1-8x)(1-9x)(1-12x)).

1, 35, 775, 13895, 220591, 3239495, 45114175, 605081015, 7896440431, 100983137255, 1271943884575, 15837914099735, 195494604120271, 2397051804927815, 29242027752046975, 355340314794184055, 4305125050033912111, 52039828472216683175, 627954645427055761375

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..925

Index entries for linear recurrences with constant coefficients, signature (35,-450,2520,-5184).

Formula

a(n) = 8^(n+2) - 9^(n+2) + 2*12^(n+1) - 6^(n+1). - R. J. Mathar, Mar 14 2011

a(n) = 35*a(n-1) - 450*a(n-2) + 2520*a(n-3) - 5184*a(n-4); a(0)=1, a(1)=35, a(2)=775, a(3)=13895. - Vincenzo Librandi, Mar 14 2011

Mathematica

CoefficientList[Series[1/((1-6x)(1-8x)(1-9x)(1-12x)), {x, 0, 20}], x] (* Harvey P. Dale, Mar 13 2025 *)
(* Alternative: *)
LinearRecurrence[{35, -450, 2520, -5184}, {1, 35, 775, 13895}, 20] (* Harvey P. Dale, Mar 13 2025 *)

Prog

(PARI) a(n)=64*8^n-81*9^n+24*12^n-6*6^n \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Sequence in context: A028220 A334909 A028213 * A028196 A028208 A028194

Adjacent sequences: A028209 A028210 A028211 * A028213 A028214 A028215

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved