

A045947


Triangles in open triangular matchstick arrangement (triangle minus one side) of side n.


8



0, 0, 2, 7, 17, 33, 57, 90, 134, 190, 260, 345, 447, 567, 707, 868, 1052, 1260, 1494, 1755, 2045, 2365, 2717, 3102, 3522, 3978, 4472, 5005, 5579, 6195, 6855, 7560, 8312, 9112, 9962, 10863, 11817, 12825, 13889, 15010, 16190, 17430, 18732, 20097, 21527
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OFFSET

0,3


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3, 2, 2, 3, 1).


FORMULA

G.f.: (2*x^2+x^3)/((1x)^3*(1x^2)).  Michael Somos
a(n) = (1/16)*(2*n*(2*n^2+n2)+(1)^n1).  Bruno Berselli, Aug 29 1011


PROG

(PARI) a(n)=(4*n^3+2*n^24*n)\16
(MAGMA) [Floor((4*n^3+2*n^24*n)/16): n in [0..50]]; // Vincenzo Librandi, Aug 29 2011


CROSSREFS

First differences of A082289.
Sequence in context: A086513 A166381 A083723 * A145066 A014148 A070070
Adjacent sequences: A045944 A045945 A045946 * A045948 A045949 A045950


KEYWORD

nonn,easy,nice


AUTHOR

R. K. Guy


STATUS

approved



