A055988 - OEIS

A055988

Sequence is its own 4th difference.

1, 2, 7, 26, 95, 345, 1252, 4544, 16493, 59864, 217286, 788674, 2862617, 10390321, 37713313, 136886433, 496850954, 1803399103, 6545722210, 23758733815, 86236081273, 313007493212, 1136110191472, 4123691589365, 14967590689568

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OFFSET

1,2

COMMENTS

Row sums of Riordan array (1/(1-x), x/(1-x)^4), A109960. - Paul Barry, Jul 06 2005

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) = 5a(n-1) - 6a(n-2) + 4a(n-3) - a(n-4) = a(n-1) + A055991(n-1) = A055989(n) - A055989(n-1) = A055990(n) - 2*A055990(n-1) + A055990(n-2).

From Paul Barry, Jul 06 2005: (Start)

G.f.: (1-x)^3/(1 - 5x + 6x^2 - 4x^3 + x^4);

a(n) = Sum_{k=0..n} binomial(n+3k, 4k). (End)

MATHEMATICA

CoefficientList[Series[(1-x)^3/(1-5x+6x^2-4x^3+x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 05 2012 *)

LinearRecurrence[{5, -6, 4, -1}, {1, 2, 7, 26}, 30] (* Harvey P. Dale, Jan 15 2017 *)

PROG

(Magma) I:=[1, 2, 7, 26]; [n le 4 select I[n] else 5*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Apr 05 2012

CROSSREFS

Cf. A055989, 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: A289449 A188860 A129273 * A371798 A275013 A278351

Adjacent sequences: A055985 A055986 A055987 * A055989 A055990 A055991

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, Jun 02 2000

EXTENSIONS

More terms from James A. Sellers, Jun 05 2000

STATUS

approved