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A052244
Partial sums of A014827.
3
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.
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
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Jan 31 2000
STATUS
approved