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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

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (3, 0, -6, 3, 3, -2).

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

Adjacent sequences:  A140988 A140989 A140990 * A140992 A140993 A140994

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Jul 08 2008

EXTENSIONS

Definition corrected by D. S. McNeil, Mar 21 2009

STATUS

approved

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Last modified August 19 04:10 EDT 2019. Contains 326109 sequences. (Running on oeis4.)