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A081674 Generalized Poly-Bernoulli numbers. 3
0, 1, 6, 29, 130, 561, 2366, 9829, 40410, 164921, 669526, 2707629, 10919090, 43942081, 176565486, 708653429, 2841788170, 11388676041, 45619274246, 182670807229, 731264359650, 2926800830801, 11712433499806, 46865424529029 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of A027649. Inverse binomial transform of A081675

With offset 1, partial sums of A085350. - Paul Barry, Jun 24 2003

Number of walks of length 2n+2 between two nodes at distance 4 in the cycle graph C_12. - Herbert Kociemba, Jul 05 2004

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (8,-19,12).

FORMULA

a(n) = ((4^(n+1)-1)/3-3^n)/2 = (4*4^n-3*3^n-1)/6.

a(n) = (A002450(n+1)+A000244(n))/2.

G.f.: x*(1-2*x)/((1-x)*(1-3*x)*(1-4*x)).

MATHEMATICA

Join[{a=0, b=1}, Table[c=7*b-12*a-1; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 19 2011*)

PROG

(MAGMA) [((4^(n+1)-1)/3-3^n)/2: n in [0..30]]; // Vincenzo Librandi, Jul 17 2011

CROSSREFS

Sequence in context: A081278 A054146 A172062 * A173413 A008549 A026675

Adjacent sequences:  A081671 A081672 A081673 * A081675 A081676 A081677

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 28 2003

STATUS

approved

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Last modified October 17 01:24 EDT 2018. Contains 316275 sequences. (Running on oeis4.)