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A081591
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Third row of Pascal-(1,6,1) array A081581.
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2
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1, 15, 78, 190, 351, 561, 820, 1128, 1485, 1891, 2346, 2850, 3403, 4005, 4656, 5356, 6105, 6903, 7750, 8646, 9591, 10585, 11628, 12720, 13861, 15051, 16290, 17578, 18915, 20301, 21736, 23220, 24753, 26335, 27966, 29646, 31375, 33153, 34980
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OFFSET
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0,2
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COMMENTS
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1.Smallest triangular number T(k) (other than the trivial adjacent ones) such that T(n) + T(k) is a square. ( T(n-1) and T(n+1) are trivial triangular numbers such that T(n) +T(n-1) and T(n) + T(n+1) both are squares.) 0+1 = 1, 1+15 = 16, 3+ 78= 81, 6 + 190 = 196 etc. 2. (7n+5)-th triangular number. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 20 2003
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..2000
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FORMULA
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a(n) = (2-21*n+49*n^2)/2.
G.f.: (1+6*x)^2/(1-x)^3.
a(0)=1, a(1)=15, a(2)=78, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) -- From Harvey P. Dale, Aug 03 2012
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MATHEMATICA
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Table[(2-21n+49n^2)/2, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 15, 78}, 40] (* Harvey P. Dale, Aug 03 2012 *)
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PROG
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(MAGMA) [(2-21*n+49*n^2)/2: n in [0..50]]; // Vincenzo Librandi, Jun 18 2011
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CROSSREFS
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Cf. A016993, A081592.
Sequence in context: A205433 A128272 A180579 * A044202 A044583 A212746
Adjacent sequences: A081588 A081589 A081590 * A081592 A081593 A081594
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Mar 23 2003
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STATUS
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approved
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