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A046174 Indices of pentagonal numbers which are also triangular. 10
0, 1, 12, 165, 2296, 31977, 445380, 6203341, 86401392, 1203416145, 16761424636, 233456528757, 3251629977960, 45289363162681, 630799454299572, 8785902997031325, 122371842504138976, 1704419892060914337 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..500

W. Sierpiński, Sur les nombres pentagonaux, Bull. Soc. Roy. Sci. Liège 33 (1964) 513-517.

W. Sierpiński, Sur les nombres pentagonaux, Bull. Soc. Roy. Sci. Liège 33 (1964) 513-517.

Eric Weisstein's World of Mathematics, Pentagonal Triangular Number.

Index entries for linear recurrences with constant coefficients, signature (15,-15,1)

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*sqrt(12*a(n)^2 - 4*a(n) + 1). - Richard Choulet, 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. - 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. - Sture Sjöstedt, May 29 2009

MATHEMATICA

LinearRecurrence[{15, -15, 1}, {0, 1, 12}, 20] (* Harvey P. Dale, Aug 22 2011 *)

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

CROSSREFS

Cf. A014979, A046175, A001834.

Sequence in context: A231541 A203372 A193104 * A055760 A056591 A190063

Adjacent sequences:  A046171 A046172 A046173 * A046175 A046176 A046177

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified October 18 20:07 EDT 2019. Contains 328197 sequences. (Running on oeis4.)