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A369838 Number of compositions of 5*n-3 into parts 1 and 5. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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. A003520.
Sequence in context: A271752 A291244 A290910 * A070071 A285363 A356942
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 03 2024
STATUS
approved

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Last modified June 17 12:36 EDT 2024. Contains 373445 sequences. (Running on oeis4.)