A052150 Partial sums of A000340, second partial sums of A003462.

1, 6, 24, 82, 261, 804, 2440, 7356, 22113, 66394, 199248, 597822, 1793557, 5380776, 16142448, 48427480, 145282593, 435847950, 1307544040, 3922632330, 11767897221, 35303691916, 105911076024, 317733228372, 953199685441

Offset: 0

Author

Barry E. Williams, Jan 23 2000

Keywords

• easy
• nonn

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.
• P. Ribenhoim, The Little Book of Big Primes, Springer-Verlag, N.Y., 1991, p. 53.

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-12,10,-3).

Crossrefs

Cf. A003462, A000340.

Programs

Mathematica

LinearRecurrence[{6,-12,10,-3},{1,6,24,82},40] (* Harvey P. Dale, Sep 05 2013 *)

Formula

a(n) = ((3^(n+3)) - (2*(n^2) + 12n + 19))/8.

a(n) = 3a(n-1)+C(n+2,2); a(0)=1.

a(n) = sum{k=0..n, binomial(n+3, k+3)2^k}. - Paul Barry, Aug 20 2004

From Colin Barker, Dec 18 2012: (Start)

a(n) = 6*a(n-1) - 12*a(n-2) + 10*a(n-3) - 3*a(n-4).

G.f.: 1/((x-1)^3*(3*x-1)). (End)