

A055989


a(n) is its own 4th difference.


4



1, 3, 10, 36, 131, 476, 1728, 6272, 22765, 82629, 299915, 1088589, 3951206, 14341527, 52054840, 188941273, 685792227, 2489191330, 9034913540, 32793647355, 119029728628, 432037221840, 1568147413312, 5691839002677
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OFFSET

1,2


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (5,6,4,1).


FORMULA

a(n) = 5*a(n1)  6*a(n2) + 4*a(n3)  a(n4) = a(n1) + A055988(n) = A055990(n)  A055990(n1) = A055991(n)  2*A055991(n1) + A055991(n2).
G.f.: x*(1x)^2/(1  5*x + 6*x^2  4*x^3 + x^4).  Colin Barker Apr 04 2012


MATHEMATICA

CoefficientList[Series[(1x)^2/(15*x+6*x^24*x^3+x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 05 2012 *)
LinearRecurrence[{5, 6, 4, 1}, {1, 3, 10, 36}, 30] (* Harvey P. Dale, Jan 10 2014 *)


PROG

(MAGMA) I:=[1, 3, 10, 36]; [n le 4 select I[n] else 5*Self(n1)6*Self(n2)+4*Self(n3)Self(n4): n in [1..30]]; // Vincenzo Librandi, Apr 05 2012


CROSSREFS

Cf. A055988, A055990, A055991 for the other differences of a(n). See A000079, A001906, A052529 for examples of sequences which are respectively their own first, second and third differences.
Sequence in context: A047122 A047107 A149040 * A102871 A277287 A119374
Adjacent sequences: A055986 A055987 A055988 * A055990 A055991 A055992


KEYWORD

nonn,easy


AUTHOR

Henry Bottomley, Jun 02 2000


EXTENSIONS

More terms from James A. Sellers, Jun 05 2000


STATUS

approved



