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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 (list; graph; refs; listen; history; text; internal format)
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)/((1-x)^3*(1-x^2)). - Michael Somos

a(n) = (1/16)*(2*n*(2*n^2+n-2)+(-1)^n-1). - Bruno Berselli, Aug 29 1011

PROG

(PARI) a(n)=(4*n^3+2*n^2-4*n)\16

(MAGMA) [Floor((4*n^3+2*n^2-4*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

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Last modified August 29 10:37 EDT 2015. Contains 261188 sequences.