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

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,6,-6).

Crossrefs

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

Cf. A026565, A233325.

Programs

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

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 *)

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

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