A369838 Number of compositions of 5*n-3 into parts 1 and 5.

1, 4, 15, 60, 245, 1001, 4085, 16665, 67985, 277350, 1131476, 4615966, 18831276, 76823991, 313410816, 1278589392, 5216127688, 21279691689, 86812537085, 354160046356, 1444829775128, 5894321227301, 24046447082350, 98099780277675, 400207434286276, 1632684497403029

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,-10,10,-5,1).

Formula

a(n) = A003520(5*n-3).

a(n) = Sum_{k=0..n} binomial(n+1+4*k,n-1-k).

a(n) = 6*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: x*(1-x)^2/((1-x)^5 - x).

Mathematica

LinearRecurrence[{6, -10, 10, -5, 1}, {1, 4, 15, 60, 245}, 50] (* Paolo Xausa, Mar 15 2024 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+1+4*k, n-1-k));

Crossrefs

Cf. A079675, A369836, A369837, A369839.

Cf. A003520.

Sequence in context: A271752 A291244 A290910 * A070071 A285363 A356942

Adjacent sequences: A369835 A369836 A369837 * A369839 A369840 A369841

Keyword

nonn

Author

Seiichi Manyama, Feb 03 2024

Status

approved