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A130612 Sum of the first 10^n squares. 0
1, 385, 338350, 333833500, 333383335000, 333338333350000, 333333833333500000, 333333383333335000000, 333333338333333350000000, 333333333833333333500000000, 333333333383333333335000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..10.

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

Sequence in context: A237102 A264421 A063390 * A060721 A116316 A213115

Adjacent sequences:  A130609 A130610 A130611 * A130613 A130614 A130615

KEYWORD

nonn

AUTHOR

Cino Hilliard, Jun 18 2007

EXTENSIONS

Offset corrected by Robert Israel, Jan 02 2015

STATUS

approved

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Last modified December 4 03:26 EST 2016. Contains 278745 sequences.