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A081498
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In the following triangle the n-th row starts with n, contains n terms and the difference of successive terms is 1,2,3.. up to n-1. Sequence gives row sums.
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1
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1, 3, 5, 6, 5, 1, -7, -20, -39, -65, -99, -142, -195, -259, -335, -424, -527, -645, -779, -930, -1099, -1287, -1495, -1724, -1975, -2249, -2547, -2870, -3219, -3595, -3999, -4432, -4895, -5389, -5915, -6474, -7067, -7695, -8359, -9060, -9799, -10577, -11395, -12254, -13155, -14099, -15087, -16120
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 1
2 1
3 2 0
4 3 1 -2
5 4 2 -1 -5
6 5 3 0 -4 -9
7 6 4 1 -3 -8 -14
The leading diagonal is given by A080956(n) = ((n+1)(2-n)/2).
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FORMULA
| a(n) = (n+1)^2-binomial(n+2, n-1) - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 20 2004
binomial(n,2)+binomial(n,1)-binomial(n,3), n>=1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 23 2006
a(n) = -(n+1)*(n^2-4*n-6)/6 - Karen Yeats (kayeats(AT)bu.edu), Nov 20 2006
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MAPLE
| seq((n+1)^2-binomial(n+2, n-1), n=0..50); (C. Ronaldo)
[seq(binomial(n, 2)+binomial(n, 1)-binomial(n, 3), n=1..49)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 23 2006
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CROSSREFS
| Cf. A080956, A081499.
Sequence in context: A078064 A091517 A106117 * A110279 A161435 A077859
Adjacent sequences: A081495 A081496 A081497 * A081499 A081500 A081501
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KEYWORD
| sign
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 25 2003
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EXTENSIONS
| More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 20 2004
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