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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 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

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