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A130615
Sum of the first 10^n 4th powers.
1
1, 25333, 2050333330, 200500333333300, 20005000333333333000, 2000050000333333333330000, 200000500000333333333333300000, 20000005000000333333333333333000000, 2000000050000000333333333333333330000000, 200000000500000000333333333333333333300000000
OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (111010,-1111110000,1011100000000,-10000000000000).
FORMULA
Sum of the first m fourth powers = m(m+1)(2m+1)(3m^2+3m-1)/30 (see A000538).
From Colin Barker, Jun 14 2015: (Start)
a(n) = A000538(10^n).
a(n) = 2^(-5+n) * 5^(-6+n) * (-5000 + 4^(1+n)*5^(3+2*n) + 3*5^(2+3*n)*8^n+3*10^(4*n))/3.
a(n) = 111010*a(n-1) - 1111110000*a(n-2) + 1011100000000*a(n-3) - 10000000000000*a(n-4).
G.f.: x*(29480000000*x^3+349227000*x^2-85677*x+1) / ((10*x-1)*(1000*x-1)*(10000*x-1)*(100000*x-1)).
(End)
PROG
(PARI) sumquartic(n) = { for(x=0, n, m=10^x; z=m*(m+1)*(2*m+1)*(3*m^2+3*m-1)/30; (print1(z", "))) }
(PARI) Vec(x*(29480000000*x^3+349227000*x^2-85677*x+1) / ((10*x-1)*(1000*x-1)*(10000*x-1)*(100000*x-1)) + O(x^15)) \\ Colin Barker, Jun 14 2015
CROSSREFS
Sequence in context: A179723 A174825 A269041 * A175741 A203090 A251227
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Jun 18 2007
STATUS
approved