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A052149
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Nonsquare rectangles on an n X n board.
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4
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0, 4, 22, 70, 170, 350, 644, 1092, 1740, 2640, 3850, 5434, 7462, 10010, 13160, 17000, 21624, 27132, 33630, 41230, 50050, 60214, 71852, 85100, 100100, 117000, 135954, 157122, 180670, 206770, 235600, 267344, 302192, 340340, 381990, 427350, 476634
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
| a(n) = n*(n-1)*(n+1)*(3*n+2)/12.
a(n) = A000537(n)-A000330(n) = 2*A000914(n+1).
G.f.: 2*x^2*(2+x)/(1-5*x+10*x^2-10*x^3+5*x^4-x^5). - Colin Barker, Jan 04 2012
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EXAMPLE
| a(10) = 10 * 9 * 11 * 32 / 12 = 2640
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MAPLE
| a:=n->sum(j^3-j^2, j=0..n): seq(a(n), n=1..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2008
a:=n->sum((n-j)^3-(n-j)^2, j=1..n): seq(a(n), n=2..38); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 26 2008
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MATHEMATICA
| a[n_]:=n^2; b[n_]:=n^3; c[n_]:=b[n]-a[n]; lst={}; s=0; Do[AppendTo[lst, s+=c[n]], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 03 2009]
s = 0; lst = {s}; Do[s += n^3 - n^2; AppendTo[lst, s], {n, 2, 37, 1}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 15 2009]
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CROSSREFS
| Cf. A035291.
Sequence in context: A174814 A106846 A086863 * A062966 A201127 A078155
Adjacent sequences: A052146 A052147 A052148 * A052150 A052151 A052152
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KEYWORD
| nonn,easy
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AUTHOR
| Ronald Arms (ron.arms(AT)stanfordalumni.org), Jan 23 2000
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