A201008 Triangular numbers, T(m), that are five-sixths of another triangular number: T(m) such that 6*T(m)=5*T(k) for some k.

0, 55, 26565, 12804330, 6171660550, 2974727580825, 1433812522297155, 691094661019647940, 333106192798948009980, 160556493834431921162475, 77387896922003387052303025, 37300805759911798127288895630

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..229

Index entries for linear recurrences with constant coefficients, signature (483,-483,1).

Formula

For n > 1, a(n) = 482*a(n-1) - a (n-2) + 55. See A200993 for generalization.

From Bruno Berselli, Dec 21 2011: (Start)

G.f.: 55*x/((1-x)*(1-482*x+x^2)).

a(n) = a(-n-1) = 483*a(n-1)-483*a(n-2)+a(n-3).

a(n) = ((11-2r))^(2n+1)+(11+2r)^(2n+1)-22)/192, where r=sqrt(30). (End)

Example

6*0 = 5*0;
6*55 = 5*66;
6*26565 = 5*31878;
6*12804330 = 5*15365196.

Mathematica

LinearRecurrence[{483, -483, 1}, {0, 55, 26565}, 30] (* Vincenzo Librandi, Dec 22 2011 *)

Prog

(Maxima) makelist(expand(((11-2*sqrt(30))^(2*n+1)+(11+2*sqrt(30))^(2*n+1)-22)/192), n, 0, 11); \* Bruno Berselli, Dec 21 2011 *\
(Magma) I:=[0, 55, 26565]; [n le 3 select I[n] else 483*Self(n-1)-483*Self(n-2)+Self(n-3): n in [1..15]]; // Vincenzo Librandi, Dec 22 2011
(PARI) concat(0, Vec(55/(1-x)/(1-482*x+x^2)+O(x^98))) \\ Charles R Greathouse IV, Dec 23 2011

Crossrefs

Cf. A001652, A029549, A053141, A075528, A200993-A201008.

Sequence in context: A163036 A358785 A033512 * A172722 A221000 A196428

Adjacent sequences: A201005 A201006 A201007 * A201009 A201010 A201011

Keyword

nonn,easy,changed

Author

Charlie Marion, Dec 20 2011

Extensions

a(11) corrected by Bruno Berselli, Dec 21 2011

a(6) corrected by Vincenzo Librandi, Dec 22 2011

Status

approved