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A115006
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Row 2 of array in A114999.
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5
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0, 3, 8, 16, 26, 39, 54, 72, 92, 115, 140, 168, 198, 231, 266, 304, 344, 387, 432, 480, 530, 583, 638, 696, 756, 819, 884, 952, 1022, 1095, 1170, 1248, 1328, 1411, 1496, 1584, 1674, 1767, 1862, 1960, 2060, 2163, 2268, 2376, 2486, 2599, 2714, 2832, 2952, 3075, 3200
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Number of lattice points (x,y) in the region of the coordinate plane bounded by y < 3x+1, y > x/2 and x <= n. - Wesley Ivan Hurt, Oct 27 2014
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
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FORMULA
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a(n) = Floor((n+1)^2/4)+n*(n+1).
G.f.: x*(2*x+3)/((1-x)^3*(1+x)).
From Wesley Ivan Hurt, Oct 27 2014: (Start)
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4).
a(n) = (10*n^2 + 12*n + 1 - (-1)^n)/8.
a(n) = sum_{i=1..n+1} (10*i + (-1)^i - 9)/4. (End)
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MAPLE
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A115006:=n->(10*n^2 + 12*n + 1 - (-1)^n)/8: seq(A115006(n), n=0..50); # Wesley Ivan Hurt, Oct 27 2014
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MATHEMATICA
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Table[(10*n^2 + 12*n + 1 - (-1)^n)/8, {n, 0, 50}] (* Wesley Ivan Hurt, Oct 27 2014 *)
LinearRecurrence[{2, 0, -2, 1}, {0, 3, 8, 16}, 60] (* Harvey P. Dale, Jan 13 2015 *)
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PROG
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(Magma) [ n*(n+1) + (n+1)^2 div 4: n in [0..50] ];
(PARI) {for(n=0, 50, print1(n*(n+1)+floor((n+1)^2/4), ", "))}
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CROSSREFS
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Cf. A114999, A000217 (triangular numbers), A002620 (quarter-squares), A001859 (triangular numbers plus quarter-squares), A017305 (10n+3), A147874 (zero followed by partial sums of A017305).
Partial Sums of A047218.
Sequence in context: A122794 A225268 A211481 * A211480 A122796 A104249
Adjacent sequences: A115003 A115004 A115005 * A115007 A115008 A115009
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Feb 23 2006
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EXTENSIONS
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Edited by Klaus Brockhaus, Nov 18 2008
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STATUS
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approved
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