OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1110, -111000, 1000000).
FORMULA
Sum of the first m squares = m(2m^2+3m+1)/6.
From Robert Israel, Jan 02 2015: (Start)
a(n) = (2*10^(3*n)+3*10^(2*n)+10^n)/6.
a(n+3) = 10^6*a(n) - 111000*a(n+1) + 1110*a(n+2)
G.f.: 1/(3 - 3000*x) + 1/(2 - 200*x) + 1/(6 - 60*x).
E.g.f.: exp(1000*x)/3 + exp(100*x)/2 + exp(10*x)/6.
(End)
MAPLE
seq((2*10^(3*n)+3*10^(2*n)+10^n)/6, n = 0 .. 30); # Robert Israel, Jan 02 2015
MATHEMATICA
Table[(2^(x-1)*5^x*(1+2^(x+1)*5^x)(1+10^x))/3, {x, 0, 20}] (* or *) Join[{1}, LinearRecurrence[{1110, -111000, 1000000}, {385, 338350, 333833500}, 20]] (* or *) Join[{1}, Table[FromDigits[Join[PadRight[{}, n, 3], {8}, PadRight[{}, n-1, 3], {5}, PadRight[{}, n-1, 0]]], {n, 20}]] (* Harvey P. Dale, Jan 02 2015 *)
PROG
(PARI) sumsq(n) = for(x=0, n, y=10^x; z=y*(y+1)*(2*y+1)/6; (print1(z", "))) \\Trust but verify, brute force sum
g1(n) = for(x=0, n, y=sum(j=1, 10^x, j^2); (print1(y", ")))
CROSSREFS
KEYWORD
nonn
AUTHOR
Cino Hilliard, Jun 18 2007
EXTENSIONS
Offset corrected by Robert Israel, Jan 02 2015
STATUS
approved