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Search: id:A054000
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| 0, 6, 16, 30, 48, 70, 96, 126, 160, 198, 240, 286, 336, 390, 448, 510, 576, 646, 720, 798, 880, 966, 1056, 1150, 1248, 1350, 1456, 1566, 1680, 1798, 1920, 2046, 2176, 2310, 2448, 2590, 2736, 2886, 3040, 3198, 3360, 3526, 3696, 3870, 4048, 4230, 4416
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = number of edges in (n+1) X (n+1) square grid with all horizontal, vertical and great diagonal segments filled in.
Sequence allows us to find X values of the equation: 2*X^3 + 4*X^2 = Y^2. To find Y values: b(n)=2n(2*n^2 - 2). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007
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FORMULA
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a(n)=A067725-A005563. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 06 2007
a(n)=4*n+a(n-1)-2 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
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EXAMPLE
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For n=2, a(2)=4*2+0-2=6; n=3, a(3)=4*3+6-2=16; n=4, a(4)=4*4+16-2=30 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
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MAPLE
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[ seq(2*n^2 - 2, n=1..60) ];
a:=n->sum(n+2*j, j=2..n): seq(a(n), n=1..47); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2007
with(finance):seq(add(cashflows([n, k, k], 0 ), k=2..n), n=1..51); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2008
a:=n->sum(2+sum(2, k=1..n), k=2..n):seq(a(n), n=1...43); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 24 2008]
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MATHEMATICA
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s=0; lst={}; Do[s+=n+n-4; If[s>=0, AppendTo[lst, s]], {n, 1, 5!, 2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 04 2008]
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CROSSREFS
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Cf. A046092, A002943.
a(n)=A100345(n+1, n-4) for n>2.
Cf. A005563, A067725.
Cf. A005563, A046092, A001082, A002378, A036666, A062717, A028347, A087475, A000217, A056220.
Sequence in context: A017341 A088818 A032422 this_sequence A113742 A102214 A115007
Adjacent sequences: A053997 A053998 A053999 this_sequence A054001 A054002 A054003
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KEYWORD
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nonn,new
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AUTHOR
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Asher Auel (asher.auel(AT)reed.edu) Jan 12, 2000
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