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A027271 a(n) = Sum_{k=0..2n} (k+1)*T(n,k), where T is given by A026536. 1
1, 4, 18, 48, 180, 432, 1512, 3456, 11664, 25920, 85536, 186624, 606528, 1306368, 4199040, 8957952, 28553472, 60466176, 191476224, 403107840, 1269789696, 2660511744, 8344332288, 17414258688, 54419558400, 113192681472 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (0,12,0,-36).

FORMULA

G.f.: (1+4x+6x^2)/(1-6x^2)^2 = dif((1+3x)/(1-6x^2), x); a(n)=6^(n/2)((sqrt(3)-sqrt(2))(-1)^n+(sqrt(3)+sqrt(2)))(n+1)sqrt(3)/6. - Paul Barry, Mar 03 2004

a(n) = 4*b(n) + b(n+1) +6*b(n-1) with b(n)= 0,1,0,12,0,108,0,864,... (aerated A053469). - R. J. Mathar, Sep 29 2012

PROG

(PARI) A027271(n)=my(b(n)=if(!bittest(n, 0), n\2*6^(n\2-1))); 4*b(n+1)+b(n+2)+6*b(n) \\ could be made more efficient and explicit by simplifying the formula for n even and for n odd separately. - M. F. Hasler, Sep 29 2012

CROSSREFS

Cf. A199299 (bisection).

Sequence in context: A228108 A259451 A181860 * A073991 A052642 A102928

Adjacent sequences:  A027268 A027269 A027270 * A027272 A027273 A027274

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified July 14 10:07 EDT 2020. Contains 335721 sequences. (Running on oeis4.)