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A006454
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Solution to a Diophantine equation: each term is a triangular number and each term + 1 is a square.
(Formerly M3004)
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4
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0, 3, 15, 120, 528, 4095, 17955, 139128, 609960, 4726275, 20720703, 160554240, 703893960, 5454117903, 23911673955, 185279454480, 812293020528, 6294047334435, 27594051024015, 213812329916328, 937385441796000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| A. J. Gottlieb, How four dogs meet in a field, etc., Technology Review, Jul/August 1973 pp. 73-74.
J. O. Shallit, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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.
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FORMULA
| a(n) = A006451(n)*(A006451(n)+1)/2.
a(n) = A006452(n)^2 - 1 [From Joerg Arndt, Mar 4 2011].
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MAPLE
| A006454:=-3*z*(1+4*z+z**2)/(z-1)/(z**2-6*z+1)/(z**2+6*z+1); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Clear[a]; a[0]=a[1]=1; a[2]=2; a[3]=4; a[n_]:=6a[n-2]-a[n-4]; Array[a, 40]^2-1 (*From Vladimir Joseph Stephan Orlovsky, Mar 03 2011*)
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CROSSREFS
| Sequence in context: A060639 A068052 A068859 * A112228 A093571 A093570
Adjacent sequences: A006451 A006452 A006453 * A006455 A006456 A006457
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit
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EXTENSIONS
| Better description from Harvey P. Dale (hpd1(AT)nyu.edu), Jan 28 2001.
More terms from Larry Reeves (larryr(AT)acm.org), Feb 07 2001
Minor edits by N. J. A. Sloane, Oct 24 2009
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