A052244 Partial sums of A014827.

1, 8, 46, 240, 1215, 6096, 30508, 152576, 762925, 3814680, 19073466, 95367408, 476837131, 2384185760, 11920928920, 59604644736, 298023223833, 1490116119336, 7450580596870, 37252902984560, 186264514923031, 931322574615408, 4656612873077316, 23283064365386880

Offset: 0

Author

Barry E. Williams, Jan 31 2000

Keywords

• easy
• nonn

References

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

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-18,16,-5).

Crossrefs

Cf. A014827, A003463, A000351.

Programs

Mathematica

LinearRecurrence[{8,-18,16,-5},{1,8,46,240},20] (* Harvey P. Dale, Jun 19 2022 *)

Formula

a(n) = ((5^(n+3))-(8*(n^2) + 44*n + 61))/64.

a(n) = 5a(n-1)+ C(n+2, 2), n >= 0; a(-1)=0.

G.f.: 1 / ( (5*x-1)*(x-1)^3 ). - R. J. Mathar, Nov 19 2014