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A077866 Expansion of (1-x)^(-1)/(1 - x - 2*x^2 + 2*x^3). 6
1, 2, 5, 8, 15, 22, 37, 52, 83, 114, 177, 240, 367, 494, 749, 1004, 1515, 2026, 3049, 4072, 6119, 8166, 12261, 16356, 24547, 32738, 49121, 65504, 98271, 131038, 196573, 262108, 393179, 524250, 786393, 1048536, 1572823, 2097110, 3145685, 4194260, 6291411, 8388562 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Equals triangle A122196 * [1,2,4,8,16,...]. - Gary W. Adamson, Nov 29 2008
Conjecture: let b(n) be the number of subsets S of {1,2,...,n} having more than one element such that (sum of least two elements of S) = max(S). Then b(0) = b(1) = b(2) = 0 and b(n+3) = a(n) for n >= 0. - Clark Kimberling Sep 27 2022
LINKS
FORMULA
a(n) = 2^(n/2)*(3 + 2*sqrt(2) + (3 - 2*sqrt(2))*(-1)^n) - n - 5. - Paul Barry, Apr 23 2004
a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + 2*a(n-4); a(0)=1, a(1)=2, a(2)=5, a(3)=8. - Harvey P. Dale, Feb 16 2013
a(2n) = 3*2^(n+1) - 2(n+1) - 3 = A050488(n+1) and a(2n+1) = 2^(n+3) - 2(n+3) = A005803(n+3). Also, a(2n+1) - a(2n) = 2^(n+1) - 1 = a(2n) - a(2n - 1). - Gregory L. Simay, Feb 07 2021
E.g.f.: 6*cosh(sqrt(2)*x) + 4*sqrt(2)*sinh(sqrt(2)*x) - exp(x)*(5 + x). - Stefano Spezia, Feb 08 2021
G.f.: 1/((1 - x)^2 * (1 - 2*x^2)). - Michael Somos, Aug 11 2021
EXAMPLE
G.f. = 1 + 2*x + 5*x^2 + 8*x^3 + 15*x^4 + 22*x^5 + 37*x^6 + ... - Michael Somos, Aug 11 2021
MATHEMATICA
CoefficientList[Series[(1-x)^(-1)/(1-x-2x^2+2x^3), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 1, -4, 2}, {1, 2, 5, 8}, 50] (* Harvey P. Dale, Feb 16 2013 *)
PROG
(PARI) Vec((1-x)^(-1)/(1-x-2*x^2+2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
Bisections are A005803 and A050488.
Cf. A052551 (first differences), A122196.
Sequence in context: A024808 A238619 A323285 * A098894 A121641 A349796
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved

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Last modified June 20 12:38 EDT 2024. Contains 373527 sequences. (Running on oeis4.)