A052161 Partial sums of A014825, second partial sums of A002450.

1, 7, 34, 146, 599, 2417, 9696, 38820, 155325, 621355, 2485486, 9942022, 39768179, 159072821, 636291404, 2545165752, 10180663161, 40722652815, 162890611450, 651562446010

Offset: 0

Author

Barry E. Williams, Jan 25 2000

Keywords

• easy
• nonn

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-15,13,-4)

Crossrefs

Cf. A014825, A002450, A000302.

Programs

Magma

[((2^(2*n+7))-(9*(n^2)+51*n+74))/54: n in [0..25]]; // Vincenzo Librandi, Apr 28 2012

Mathematica

CoefficientList[Series[1/((1-x)^3*(1-4*x)),{x,0,25}],x] (* Vincenzo Librandi, Apr 28 2012 *)

Formula

a(n) = ((2^(2n+7)) - (9*(n^2) + 51n + 74))/54.

a(n) = 4a(n-1) + C(n+2,2); a(0)=1.

a(n) = Sum_{k=0..n, binomial(n+3, k+3)3^k}. - Paul Barry, Aug 20 2004

G.f.: 1/((1-x)^3*(1-4*x)). - Colin Barker, Jan 12 2012