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, 36315, 38226, 40186, 42195

Offset: 0

Author

Jason Earls, Jun 22 2001

Keywords

• easy
• nonn

Comments

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

References

• D. M. Burton, Elementary Number Theory, Allyn and Bacon, Inc. Boston, MA, 1976, p. 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).

Crossrefs

Cf. A000217, A177071.

Programs

Mathematica

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

PARI

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

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

From Elmo R. Oliveira, Oct 23 2024: (Start)

G.f.: (6 + 37*x + 6*x^2)/(1 - x)^3.

E.g.f.: (6 + 49*x + 49*x^2/2)*exp(x).

a(n) = 6 + 49*A000217(n) = A177071(n)/2. (End)