OFFSET
0,2
COMMENTS
Number of ascending runs in {1,...,n}^8.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
G.f.: -(x^7+695*x^6+15570*x^5+65998*x^4+74573*x^3+23067*x^2+1528*x+8)*x/ (x-1)^9.
MAPLE
a:= n-> n^7*(9*n+7)/2:
seq(a(n), n=0..40);
MATHEMATICA
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {0, 8, 1600, 37179, 352256, 2031250, 8538048, 28824005, 82837504}, 30] (* Harvey P. Dale, Nov 18 2025 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 15 2013
STATUS
approved