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A045949
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Triangles in hexagonal matchstick arrangement of side n.
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0
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0, 6, 38, 116, 262, 496, 840, 1314, 1940, 2738, 3730, 4936, 6378, 8076, 10052, 12326, 14920, 17854, 21150, 24828, 28910, 33416, 38368, 43786, 49692, 56106, 63050, 70544, 78610, 87268, 96540, 106446, 117008, 128246, 140182, 152836, 166230
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-2,-2,3,-1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 03 2010]
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FORMULA
| a(n) = [ n(14n^2+9n+2)/4 ]
a(n)= +3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5). G.f.: 2*x*(3+10*x+7*x^2+x^3) / ( (1+x)*(x-1)^4 ). a(n) = 7*n^3/2+9*n^2/4+n/2-1/8+(-1)^n/8. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 03 2010]
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MATHEMATICA
| LinearRecurrence[{3, -2, -2, 3, -1}, {0, 6, 38, 116, 262}, 40] (* or *) CoefficientList[Series[(2*x*(x*(x+2)*(x+5)+3))/((x-1)^4*(x+1)), {x, 0, 40}], x] (* From Harvey P. Dale, June 11 2011 *)
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CROSSREFS
| Sequence in context: A055713 A060454 A060452 * A189492 A026296 A037499
Adjacent sequences: A045946 A045947 A045948 * A045950 A045951 A045952
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KEYWORD
| nonn
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AUTHOR
| R. K. Guy
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