A055989 a(n) is its own 4th difference.

1, 3, 10, 36, 131, 476, 1728, 6272, 22765, 82629, 299915, 1088589, 3951206, 14341527, 52054840, 188941273, 685792227, 2489191330, 9034913540, 32793647355, 119029728628, 432037221840, 1568147413312, 5691839002677, 20659429692245, 74986666876571, 272175964826781

Offset

1,2

Comments

Number of compositions of 4*n-3 into parts 1 and 4. - Seiichi Manyama, Feb 03 2024

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(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) = a(n-1) + A055988(n) = A055990(n) - A055990(n-1) = A055991(n) - 2*A055991(n-1) + A055991(n-2).

G.f.: x*(1-x)^2/(1 - 5*x + 6*x^2 - 4*x^3 + x^4). - Colin Barker Apr 04 2012

Mathematica

CoefficientList[Series[(1-x)^2/(1-5*x+6*x^2-4*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(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): 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.

Cf. A003269.

Sequence in context: A047122 A047107 A149040 * A329533 A102871 A371842

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