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A081674
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Generalized Poly-Bernoulli numbers.
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3
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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; internal format)
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OFFSET
| 0,3
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COMMENTS
| Binomial transform of A027649. Inverse binomial transform of A081675
With offset 1, partial sums of A085350. - Paul Barry (pbarry(AT)wit.ie), Jun 24 2003
Number of walks of length 2n+2 between two nodes at distance 4 in the cycle graph C_12. - Herbert Kociemba (kociemba(AT)t-online.de), Jul 05 2004
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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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)).
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=7*b-12*a-1; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 19 2011*)
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PROG
| (MAGMA) [((4^(n+1)-1)/3-3^n)/2: n in [0..30]]; // Vincenzo Librandi, Jul 17 2011
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CROSSREFS
| Sequence in context: A081278 A054146 A172062 * A173413 A008549 A026675
Adjacent sequences: A081671 A081672 A081673 * A081675 A081676 A081677
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 28 2003
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