A061792 a(n) = 49*(n*(n+1)/2) + 6.

6, 55, 153, 300, 496, 741, 1035, 1378, 1770, 2211, 2701, 3240, 3828, 4465, 5151, 5886, 6670, 7503, 8385, 9316, 10296, 11325, 12403, 13530, 14706, 15931, 17205, 18528, 19900, 21321, 22791, 24310, 25878, 27495, 29161, 30876, 32640, 34453

Offset

0,1

Comments

"If n is a triangular number, then so are 9n+1, 25n+3 and 49n+6. (Euler, 1775)." Burton, p. 17.

References

D. M. Burton, Elementary Number Theory, Allyn and Bacon, Inc. Boston, MA, 1976, pp. 17.

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=6, a(1)=55, a(2)=153. - Harvey P. Dale, Apr 11 2012

Mathematica

49*Accumulate[Range[0, 40]]+6 (* or *) LinearRecurrence[{3, -3, 1}, {6, 55, 153}, 40] (* Harvey P. Dale, Apr 11 2012 *)

Prog

(PARI) v=[]; for(n=0, 100, v=concat(v, 49*(n*(n+1)/2)+6)); v
(PARI) for (n=0, 1000, write("b061792.txt", n, " ", 49*n*(n + 1)/2 + 6)) \\ Harry J. Smith, Jul 28 2009

Crossrefs

Cf. A000217.

Sequence in context: A085067 A069508 A079465 * A066514 A281075 A009577

Adjacent sequences: A061789 A061790 A061791 * A061793 A061794 A061795

Keyword

easy,nonn

Author

Jason Earls, Jun 22 2001

Status

approved