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 A241862 Number of compositions of n such that the smallest part has multiplicity two. 3
 1, 0, 4, 3, 10, 18, 35, 60, 121, 217, 391, 709, 1281, 2283, 4061, 7185, 12680, 22291, 39051, 68191, 118767, 206331, 357596, 618345, 1066983, 1837513, 3158685, 5420335, 9286086, 15884155, 27130404, 46274560, 78822938, 134095757, 227853408, 386721362, 655639944 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 LINKS Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 2..1000 FORMULA a(n) ~ (1/4 - 11/(20*sqrt(5))) * n^2 * ((1+sqrt(5))/2)^n. - Vaclav Kotesovec, May 01 2014 Equivalently, a(n) ~ n^2 * phi^(n-5) / (2 * 5^(3/2)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Dec 06 2021 MAPLE b:= proc(n, s) option remember; `if`(n=0, 1, `if`(nadd(coeff(p, x, i)*binomial(i+k, k), i=0..degree(p)))(b(n-j*k, j+1)), j=1..n/k) end: seq(a(n), n=2..40); MATHEMATICA b[n_, s_] := b[n, s] = If[n == 0, 1, If[n

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Last modified July 19 04:51 EDT 2024. Contains 374388 sequences. (Running on oeis4.)