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A140991 a(n) = (1/9)*(7*2^n + (-1)^n*(3*n+2)) - (n-1)^2. 0
0, 1, 3, 1, 5, 7, 27, 61, 153, 331, 719, 1489, 3069, 6223, 12579, 25285, 50753, 101683, 203607, 407449, 815205, 1630711, 3261803, 6523981, 13048425, 26097307, 52195167, 104390881, 208782413, 417565471, 835131699, 1670264149 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
REFERENCES
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 1990, p. 327.
LINKS
FORMULA
a(n) = A006904(n) - (n-1)^2.
From R. J. Mathar, Mar 27 2009: (Start)
a(n) = 3*a(n-1) - 6*a(n-3) + 3*a(n-4) + 3*a(n-5) - 2*a(n-6).
G.f.: x*(1-8*x^2+8*x^3+7*x^4)/((-1+2*x)*(1+x)^2*(x-1)^3). (End)
EXAMPLE
a(0) = (1/9)*(7*2^0 + (-1)^0*(3*0+2)) - (0-1)^2 = (1/9)*(7*1 + 1*(0+2)) - (-1)^2 = (1/9)*(7+2) - 1 = 1 - 1 = 0.
PROG
(Magma) [ (1/9)*(7*2^n+(-1)^n*(3*n+2))-(n-1)^2: n in [0..100] ]; // Vincenzo Librandi, Dec 19 2010
CROSSREFS
Cf. A006904.
Sequence in context: A049764 A136437 A137328 * A302191 A261712 A038738
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition corrected by D. S. McNeil, Mar 21 2009
STATUS
approved

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Last modified July 18 06:32 EDT 2024. Contains 374377 sequences. (Running on oeis4.)