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A007901
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Number of minimal unavoidable n-celled pebbling configurations.
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0
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0, 0, 0, 0, 4, 22, 98, 412, 1700, 6974, 28576, 117146, 480722, 1974914, 8122084, 33435390, 137757480, 567998152, 2343472004, 9674252070, 39956606552, 165099840920, 682446679582, 2821858504062, 11671572244666, 48287711006032, 199822535773958, 827069530795224, 3423890026639184, 14176516741276534
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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REFERENCES
| R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 6.50.
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LINKS
| F. R. K. Chung, R. L. Graham, J. A. Morrison and A. M. Odlyzko, Pebbling a chessboard, Amer. Math. Monthly 102 (1995), pp. 113-123.
Google Labs, Google Labs congratulations puzzle
Marcus Kazmierczak, Google Labs Puzzles, Jul 29, 2004.
Slashdot (CmdrTaco), Google's Math Puzzle, Thu Sep 16, 2004.
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FORMULA
| G.f.: x^3*((1-3*x+x^2)*sqrt(1-4*x)-1+5*x-x^2-6*x^3)/(1-7*x+14*x^2-9*x^3) [from the Stanley reference, Joerg Arndt, Apr 20 2011]
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MAPLE
| The Maple snippet provides an alternative solution to the Google congratulations puzzle at http://www.7427466391.com. After running the Maple code, f(1) to f(4) match the puzzle, with f(5) being 1510865746 and f(6) being 6171783928.
Digits:=2000: E:=evalf(exp(1)): g:=n->trunc((E-(10^(-n)*trunc(E*10^n)))*10^(10+n)): h:=[0, 0, 0, 0, 4, 22, 98, 412, 1700]: f:=k->g(h[k+3]):
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PROG
| (Pari) x='x+O('x^44) /* that many terms */
gf=x^3*((1-3*x+x^2)*sqrt(1-4*x)-1+5*x-x^2-6*x^3)/(1-7*x+14*x^2-9*x^3);
Vec(gf) /* show terms */ /* Joerg Arndt, Apr 20 2011 */
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CROSSREFS
| Sequence in context: A036926 A079272 A197667 * A088581 A017970 A099013
Adjacent sequences: A007898 A007899 A007900 * A007902 A007903 A007904
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KEYWORD
| nonn,easy,nice
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AUTHOR
| odlyzko(AT)dtc.umn.edu (A. M. Odlyzko)
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