OFFSET
1,2
COMMENTS
Number of compositions of 4*n-2 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)+A055989(n) = A055991(n)-A055991(n-1) = A055988(n+1)-2*A055988(n)+A055988(n-1).
G.f.: x*(1-x)/(1-5*x+6*x^2-4*x^3+x^4). [Colin Barker, Apr 05 2012]
a(n) = Sum_{m=0..n-1} C(n+3m+1,n-m-1). - Vladimir Kruchinin, Nov 18 2020
MATHEMATICA
CoefficientList[Series[(1-x)/(1-5*x+6*x^2-4*x^3+x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 06 2012 *)
LinearRecurrence[{5, -6, 4, -1}, {1, 4, 14, 50}, 30] (* Harvey P. Dale, Oct 18 2015 *)
PROG
(Magma) I:=[1, 4, 14, 50]; [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 06 2012
(PARI) Vec((1-x)/(1-5*x+6*x^2-4*x^3+x^4)+O(x^99)) \\ Charles R Greathouse IV, Apr 06 2012
(Maxima)
a(n):=sum((binomial(n+3*m+1, n-m-1)), m, 0, n-1); /* Vladimir Kruchinin, Nov 18 2020 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Jun 02 2000
EXTENSIONS
More terms from James A. Sellers, Jun 05 2000
STATUS
approved