OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).
FORMULA
G.f.: -x*(3*x^4+4*x^3+11*x^2+8*x+1)/((x^2+x+1)*(x-1)^3).
a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5) for n>5.
3*a(n) = 5+2*A099837(n)+27*n*(n-1)/2 for n>0. - R. J. Mathar, Sep 02 2018
EXAMPLE
a(1) = 1: {1,2,3}.
a(2) = 10: {1,2,3}, {1,2,5}, {1,3,4}, {1,3,6}, {1,4,5}, {1,5,6}, {2,3,5}, {2,4,6}, {3,4,5}, {3,5,6}.
a(3) = 30: {1,2,3}, {1,2,6}, {1,2,9}, {1,3,5}, {1,3,8}, {1,4,7}, {1,5,6}, {1,5,9}, {1,6,8}, {1,8,9}, {2,3,4}, {2,3,7}, {2,4,6}, {2,4,9}, {2,5,8}, {2,6,7}, {2,7,9}, {3,4,5}, {3,4,8}, {3,5,7}, {3,6,9}, {3,7,8}, {4,5,6}, {4,5,9}, {4,6,8}, {4,8,9}, {5,6,7}, {5,7,9}, {6,7,8}, {7,8,9}.
MATHEMATICA
LinearRecurrence[{2, -1, 1, -2, 1}, {0, 1, 10, 30, 55, 91}, 50] (* Harvey P. Dale, Mar 27 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Aug 30 2018
STATUS
approved