A052153 Rhombi (in 3 different orientations) in a rhombus with 60-degree acute angles.

1, 9, 26, 54, 95, 151, 224, 316, 429, 565, 726, 914, 1131, 1379, 1660, 1976, 2329, 2721, 3154, 3630, 4151, 4719, 5336, 6004, 6725, 7501, 8334, 9226, 10179, 11195, 12276, 13424, 14641, 15929, 17290, 18726, 20239, 21831, 23504, 25260

Offset

1,2

Comments

See link for corrections to table in Ask Dr. Math link.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Ask Dr. Math, Finding Rhombi in a Rhombus, Source, about 2/3rds down, message dated 01/18/2000.

Ray Chandler, Corrections to table in Ask Dr. Math link.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = A000330(n) + A046092(n-1).

G.f.: x*(1 + 5*x - 4*x^2)/(1-x)^4. - Colin Barker, May 09 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 22 2012

Mathematica

Table[n*(n+1)*(2n+1)/6+2n*(n-1), {n, 50}] (* Ray Chandler, May 05 2011 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 9, 26, 54}, 40] (* Vincenzo Librandi, Jun 22 2012 *)

Prog

(Magma) I:=[1, 9, 26, 54]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 22 2012

Crossrefs

Cf. A000330, A000537, A006003, A046092.

Sequence in context: A343560 A330395 A081267 * A154560 A338548 A249275

Adjacent sequences: A052150 A052151 A052152 * A052154 A052155 A052156

Keyword

nonn,easy

Author

Tom Gray (TGray9278(AT)aol.com), Jan 24 2000

Extensions

Better description from Larry Reeves (larryr(AT)acm.org), Mar 21 2001

Corrected and extended by Ray Chandler, May 05 2011

Status

approved