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A143975
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Floor(n(n+3)/3).
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3
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1, 3, 6, 9, 13, 18, 23, 29, 36, 43, 51, 60, 69, 79, 90, 101, 113, 126, 139, 153, 168, 183, 199, 216, 233, 251, 270, 289, 309, 330, 351, 373, 396, 419, 443, 468, 493, 519, 546, 573, 601, 630, 659, 689, 720, 751, 783, 816, 849, 883, 918, 953, 989, 1026, 1063, 1101
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Fourth diagonal of A143974, associated with counting unit squares in a lattice.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..3000
Index to sequences with linear recurrences with constant coefficients, signature (2,-1,1,-2,1)
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FORMULA
| a(n)=floor(n(n+3)/3).
a(n)= 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5). G.f.: x*(-1-x-x^2+x^3)/( (1+x+x^2) * (x-1)^3) [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 05 2009]
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EXAMPLE
| Main diagonal of A143974: (0,1,3,5,8,12,...)=A000212;
2nd diagonal: (0,2,4,6,10,14,18,...)=A128422;
3rd diagonal: (1,2,5,8,11,16,21,...)=A032765;
4th diagonal: (1,3,6,9,13,18,23,...)=A143975.
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PROG
| (MAGMA) [Floor(n*(n+3)/3): n in [1..60]]; // Vincenzo Librandi, May 08 2011
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CROSSREFS
| Cf. A143974.
Sequence in context: A129403 A154287 A092847 * A005488 A048202 A014785
Adjacent sequences: A143972 A143973 A143974 * A143976 A143977 A143978
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Sep 06 2008
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