OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Alexander V. Karpov, An Informational Basis for Voting Rules, NRU Higher School of Economics. Series WP BRP "Economics/EC". 2018. No. 188.
P. A. MacMahon, Combinations derived from m identical sets of n different letters and their connexion with general magic squares, Proc. London Math. Soc., 17 (1917), 25-41. This sequence is column 3 of table f(m,n) on page 40.
Index entries for linear recurrences with constant coefficients, signature (2,1,-3,-1,1,3,-1,-2,1).
FORMULA
G.f.: -(x^6-x^5+2*x^4+2*x^3+2*x^2-x+1)/((x^2+x+1)*(x+1)^2*(x-1)^5).
EXAMPLE
a(2) = 5: (2*3*5)^2 = 900 = 10*10*9 = 15*10*6 = 15*15*4 = 25*6*6 = 25*9*4.
a(4) = 23: (2*3*5)^4 = 810000 = 100*90*90 = 100*100*81 = 135*100*60 = 150*90*60 = 150*100*54 = 150*135*40 = 150*150*36 = 225*60*60 = 225*90*40 = 225*100*36 = 225*150*24 = 225*225*16 = 250*60*54 = 250*81*40 = 250*90*36 = 250*135*24 = 375*54*40 = 375*60*36 = 375*90*24 = 375*135*16 = 625*36*36 = 625*54*24 = 625*81*16.
MAPLE
a:= n-> coeff(series(-(x^6-x^5+2*x^4+2*x^3+2*x^2-x+1)/
((x^2+x+1)*(x+1)^2*(x-1)^5), x, n+1), x, n):
seq(a(n), n=0..60);
MATHEMATICA
CoefficientList[Series[-(x^6 - x^5 + 2 x^4 + 2 x^3 + 2 x^2 - x + 1)/((x^2 + x + 1) (x + 1)^2*(x - 1)^5), {x, 0, 43}], x] (* Michael De Vlieger, Jul 02 2018 *)
LinearRecurrence[{2, 1, -3, -1, 1, 3, -1, -2, 1}, {1, 1, 5, 10, 23, 40, 73, 114, 180}, 50] (* Harvey P. Dale, Jan 08 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Apr 24 2015
STATUS
approved