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A115006 Row 2 of array in A114999. 5
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; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

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)

MAPLE

A115006:=n->(10*n^2 + 12*n + 1 - (-1)^n)/8: seq(A115006(n), n=0..50); # Wesley Ivan Hurt, Oct 27 2014

MATHEMATICA

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 *)

PROG

(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), ", "))}

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 23 2006

EXTENSIONS

Edited by Klaus Brockhaus, Nov 18 2008

STATUS

approved

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Last modified December 3 07:52 EST 2022. Contains 358512 sequences. (Running on oeis4.)