A369844 Number of compositions of 5*n-4 into parts 2 and 5.

0, 1, 4, 11, 29, 81, 235, 685, 1986, 5739, 16577, 47904, 138472, 400285, 1157071, 3344567, 9667590, 27944604, 80775310, 233485250, 674901117, 1950836005, 5638990526, 16299788815, 47115369056, 136189372297, 393662311506, 1137900943868, 3289160582291, 9507486039274

Offset

1,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (5,-9,10,-5,1).

Formula

a(n) = A001687(5*n-3).

a(n) = Sum_{k=0..floor(n/2)} binomial(n+1+3*k,n-2-2*k).

a(n) = 5*a(n-1) - 9*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

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

Mathematica

LinearRecurrence[{5, -9, 10, -5, 1}, {0, 1, 4, 11, 29}, 50] (* Paolo Xausa, Mar 15 2024 *)

Prog

(PARI) a(n) = sum(k=0, n\2, binomial(n+1+3*k, n-2-2*k));

Crossrefs

Cf. A369803, A369840, A369842, A369843.

Cf. A001687.

Sequence in context: A002878 A341341 A124861 * A351438 A110579 A361218

Adjacent sequences: A369841 A369842 A369843 * A369845 A369846 A369847

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 03 2024

Status

approved