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

0,2

Comments

From Enrique Navarrete, Nov 05 2025: (Start)

Second partial sums of A003463.

Convolution of the powers of 5 with the triangular numbers [1, 3, 6, 10, ...]. (End)

References

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

Links

Table of n, a(n) for n=0..23.

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

Formula

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

a(n) = 5*a(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

From Enrique Navarrete, Nov 04 2025 (Start):

a(n) = 8*a(n-1) - 18*a(n-2) + 16*a(n-3) - 5*a(n-4), n >= 4.

E.g.f.: exp(x)*(125*exp(4*x) - 8*x^2 - 52*x - 61)/64. (End)

Mathematica

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

Crossrefs

Cf. A014827, A003463, A000351, A000217.

Sequence in context: A190866 A026867 A026885 * A083421 A113992 A352094

Adjacent sequences: A052241 A052242 A052243 * A052245 A052246 A052247

Keyword

easy,nonn

Author

Barry E. Williams, Jan 31 2000

Status

approved