A026567 a(n) = Sum_{i=0..2*n} Sum_{j=0..i} T(i, j), where T is given by A026552.

1, 4, 13, 31, 85, 193, 517, 1165, 3109, 6997, 18661, 41989, 111973, 251941, 671845, 1511653, 4031077, 9069925, 24186469, 54419557, 145118821, 326517349, 870712933, 1959104101, 5224277605, 11754624613, 31345665637, 70527747685

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,6,-6).

Formula

a(n) = Sum_{i=0..2*n} Sum_{j=0..i} A026552(i, j).

G.f.: (1+3*x+3*x^2)/((1-x)*(1-6*x^2)). - Ralf Stephan, Feb 03 2004

a(n) = 6*a(n-2) + 7. - Philippe Deléham, Feb 24 2014

a(2*k) = A233325(k). - Philippe Deléham, Feb 24 2014

From Colin Barker, Nov 25 2016: (Start)

a(n) = (2^(n/2+2) * 3^(n/2+1) - 7)/5 for n even.

a(n) = (2^((n-1)/2) * 3^((n+5)/2) - 7)/5 for n odd. (End)

a(n) = (1/10)*(2*(1+(-1)^n)*6^((n+2)/2) + 27*(1-(-1)^n)*6^((n-1)/2) - 14). - G. C. Greubel, Dec 19 2021

Mathematica

CoefficientList[Series[(1 +3x +3x^2)/((1-x)(1-6x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 25 2014 *)
LinearRecurrence[{1, 6, -6}, {1, 4, 13}, 30] (* Harvey P. Dale, Aug 23 2014 *)

Prog

(Magma) [Truncate((2*(1+(-1)^n)*6^((n+2)/2) + 27*(1-(-1)^n)*6^((n-1)/2) -14)/10): n in [0..40]]; // G. C. Greubel, Dec 19 2021
(Sage) [(1/10)*(2*(1+(-1)^n)*6^((n+2)/2) +27*(1-(-1)^n)*6^((n-1)/2) -14) for n in (0..40)] # G. C. Greubel, Dec 19 2021

Crossrefs

Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026559, A026560, A026563, A026564, A026566, A027272, A027273, A027274, A027275, A027276.

Cf. A026565, A233325.

Sequence in context: A106337 A027998 A367010 * A218958 A226839 A270976

Adjacent sequences: A026564 A026565 A026566 * A026568 A026569 A026570

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved