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 A238630 Number of partitions of 3^n into parts that are at most 3. 2
 1, 3, 12, 75, 588, 5043, 44652, 399675, 3590508, 32294883, 290594892, 2615176875, 23536060428, 211822949523, 1906401762732, 17157601515675, 154418370594348, 1389765206208963, 12507886468460172, 112570977053880075, 1013138789998136268, 9118249099522873203 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (13,-39,27). FORMULA a(n) = [x^(3^n)] Product_{j=1..3} 1/(1-x^j). G.f.: (9*x^3+12*x^2-10*x+1)/((1-x)*(1-3*x)*(1-3^2*x)). a(n) = A001399(3^n) = round((3^n+3)^2/12). a(n) = 3*A051500(n-1) for n>=1. - Hugo Pfoertner, May 04 2024 EXAMPLE a(2) = 12: 333, 3222, 3321, 22221, 32211, 33111, 222111, 321111, 2211111, 3111111, 21111111, 111111111. MAPLE gf:= (9*x^3+12*x^2-10*x+1)/((1-x)*(1-3*x)*(1-3^2*x)): a:= n-> coeff(series(gf, x, n+1), x, n): seq(a(n), n=0..30); MATHEMATICA Round[(3^Range[0, 25] + 3)^2/12] (* Paolo Xausa, Jun 26 2024 *) CROSSREFS Row n=3 of A238016. Cf. A001399, A051500. Sequence in context: A342599 A291951 A176408 * A247330 A168366 A134524 Adjacent sequences: A238627 A238628 A238629 * A238631 A238632 A238633 KEYWORD nonn AUTHOR Alois P. Heinz, Mar 01 2014 STATUS approved

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Last modified August 8 04:35 EDT 2024. Contains 375018 sequences. (Running on oeis4.)