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A005565
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Number of walks on square lattice.
(Formerly M5087)
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1
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20, 75, 189, 392, 720, 1215, 1925, 2904, 4212, 5915, 8085, 10800, 14144, 18207, 23085, 28880, 35700, 43659, 52877, 63480, 75600, 89375, 104949, 122472, 142100
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
| 1/4*(n^4+14n^3+69n^2+136n+80). G.f.: (20-25x+14x^2-3x^3)/(1-x)^5. - Ralf Stephan, Apr 23 2004
a(n)= binomial(n+4,2)^2- binomial(n+4,1)^2. [From Gary Detlefs, Nov 22 2011]
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MAPLE
| seq(add (k^3-n^2, k =0..n), n=4..28 ); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 26 2007
A005565:=(-20+25*z-14*z**2+3*z**3)/(z-1)**5; [Conjectured by S. Plouffe in his 1992 dissertation.]
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PROG
| (PARI) a(n)=(n^4+14*n^3+69*n^2+136*n)/4+20 \\ Charles R Greathouse IV, Nov 22 2011
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CROSSREFS
| Sequence in context: A002292 A010008 A000529 * A066126 A083127 A002609
Adjacent sequences: A005562 A005563 A005564 * A005566 A005567 A005568
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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