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A046174
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Indices of pentagonal numbers which are also triangular.
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7
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0, 1, 12, 165, 2296, 31977, 445380, 6203341, 86401392, 1203416145, 16761424636, 233456528757, 3251629977960, 45289363162681, 630799454299572, 8785902997031325, 122371842504138976, 1704419892060914337
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..500
W. Sierpinski, Sur les nombres pentagonaux, Bull. Soc. Roy. Sci. Liege 33 (1964) 513-517.
Eric Weisstein's World of Mathematics, Pentagonal Triangular Number.
Index to sequences with linear recurrences with constant coefficients, signature (15,-15,1)
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FORMULA
| a(n) = 14*a(n-1) - a(n-2) - 2; g.f.: x*(1-3*x)/((1-x)*(1-14*x+x^2)) - Warut Roonguthai, Jan 05 2001
a(n+1)=7*a(n)-1+2*(12*a(n)^2-4*a(n)+1)^0.5 - Richard Choulet (richardchoulet(AT)yahoo.fr), Sep 19 2007
a(n)=(1/6)-(1/12)*sqrt(3)*{[7-4*sqrt(3)]^n-[7+4*sqrt(3)]^n}-(1/12)*{[7+4*sqrt(3)]^n+[7-4*sqrt(3)]^n }, with n>=0 [From Paolo P. Lava, Nov 25 2008]
a(n+1)=15*a(n)-15*a(n-1)+ a(n-2) a(1)=1,a(2)=12,a(3)=165 [From Sture Sjoestedt, May 29 2009]
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MATHEMATICA
| LinearRecurrence[{15, -15, 1}, {0, 1, 12}, 20] (* From Harvey P. Dale, Aug 22 2011 *)
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PROG
| (MAGMA) [ n eq 1 select 0 else n eq 2 select 1 else 14*Self(n-1)-Self(n-2)-2: n in [1..20] ]; // Vincenzo Librandi, Aug 23 2011
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CROSSREFS
| Cf. A014979, A046175, A001834.
Sequence in context: A143583 A203372 A193104 * A055760 A056591 A190063
Adjacent sequences: A046171 A046172 A046173 * A046175 A046176 A046177
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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