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A052161
Partial sums of A014825, second partial sums of A002450.
8
1, 7, 34, 146, 599, 2417, 9696, 38820, 155325, 621355, 2485486, 9942022, 39768179, 159072821, 636291404, 2545165752, 10180663161, 40722652815, 162890611450, 651562446010
OFFSET
0,2
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
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
MATHEMATICA
CoefficientList[Series[1/((1-x)^3*(1-4*x)), {x, 0, 25}], x] (* Vincenzo Librandi, Apr 28 2012 *)
PROG
(Magma) [((2^(2*n+7))-(9*(n^2)+51*n+74))/54: n in [0..25]]; // Vincenzo Librandi, Apr 28 2012
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Jan 25 2000
STATUS
approved