OFFSET
0,3
COMMENTS
Let A be the Hessenberg n X n matrix defined by A[1,j] = j mod 10, A[i,i]:=1, A[i,i-1]=-1. Then, for n >= 1, a(n)=det(A). - Milan Janjic, Jan 24 2010
LINKS
Shawn A. Broyles, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).
FORMULA
MAPLE
seq(coeff(series(x*(1-10*x^9+9*x^10)/((1-x^10)*(1-x)^3), x, n+1), x, n), n = 0..60); # G. C. Greubel, Aug 31 2019
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 45}, 60] (* G. C. Greubel, Aug 31 2019 *)
PROG
(PARI) a(n) = sum(k=0, n, k % 10); \\ Michel Marcus, Apr 28 2018
(Magma) I:=[0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 45]; [n le 11 select I[n] else Self(n-1) + Self(n-10) - Self(n-11): n in [1..61]]; // G. C. Greubel, Aug 31 2019
(Sage)
def A130488_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(x*(1-10*x^9+9*x^10)/((1-x^10)*(1-x)^3)).list()
A130488_list(60) # G. C. Greubel, Aug 31 2019
(GAP) a:=[0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 45];; for n in [12..61] do a[n]:=a[n-1]+a[n-10]-a[n-11]; od; a; # G. C. Greubel, Aug 31 2019
(Python)
def A130488(n):
a, b = divmod(n, 10)
return 45*a+(b*(b+1)>>1) # Chai Wah Wu, Jul 27 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, May 31 2007
STATUS
approved