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 A054390 Number of ways of writing n as a sum of powers of 3, each power being used at most three times. 11
 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 5, 2, 2, 4, 2, 2, 5, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 5, 2, 2, 4, 2, 2, 5, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 5, 4, 4, 7, 3, 3, 6, 3, 3, 8, 5, 5, 7, 2, 2, 4, 2, 2, 6, 4, 4, 6, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Let M be an infinite matrix with (1, 1, 1, 1, 0, 0, 0, ...) in each column shifted down thrice from the previous column (for k>0). Then A054390 = lim_{n->infinity} M^n, the left-shifted vector considered as a sequence. - Gary W. Adamson, Apr 14 2010 Conjecture: Number of ways of partitioning n into distinct parts of A038754. - R. J. Mathar, Mar 01 2023 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 Karl Dilcher, Larry Ericksen, Polynomials Characterizing Hyper b-ary Representations, J. Int. Seq., Vol. 21 (2018), Article 18.4.3. Timothy B. Flowers, Extending a Recent Result on Hyper m-ary Partition Sequences, Journal of Integer Sequences, Vol. 20 (2017), #17.6.7. FORMULA a(0)=1, a(1)=1, a(2)=1 and, for n>0, a(3n)=a(n)+a(n-1), a(3n+1)=a(n), a(3n+2)=a(n). G.f.: Product_{j >= 0} (1+x^(3^j)+x^(2*(3^j))+x^(3*(3^j))). - Emeric Deutsch, Apr 02 2006 G.f. A(x) satisfies: A(x) = (1 + x + x^2 + x^3) * A(x^3). - Ilya Gutkovskiy, Jul 09 2019 EXAMPLE a(33) = 4 because we have 33 = 27+3+3 = 27+3+1+1+1 = 9+9+9+3+3 = 9+9+9+3+1+1+1. MAPLE a[0]:=1: a[1]:=1: a[2]:=1: for n from 1 to 35 do a[3*n]:=a[n]+a[n-1]: a[3*n+1]:=a[n]: a[3*n+2]:=a[n] od: A:=[seq(a[n], n=0..104)]; # Emeric Deutsch, Apr 02 2006 g:=product((1+x^(3^j)+x^(2*(3^j))+x^(3*(3^j))), j=0..10): gser:=series(g, x=0, 125): seq(coeff(gser, x, n), n=0..104); # Emeric Deutsch, Apr 02 2006 # third Maple program: b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<0, 0, add(`if`(n-j*3^i<0, 0, b(n-j*3^i, i-1)), j=0..3))) end: a:= n-> b(n, ilog[3](n)): seq(a(n), n=0..100); # Alois P. Heinz, Jun 21 2012 MATHEMATICA a[0]=1; a[1]=1; a[2]=1; For[n=1, n <= 35, n++, a[3*n] = a[n] + a[n-1]; a[3*n+1] = a[n]; a[3*n+2] = a[n]]; Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Dec 20 2016, after Emeric Deutsch *) CROSSREFS Cf. A002487. Sequence in context: A284312 A261612 A184241 * A161068 A161107 A161042 Adjacent sequences: A054387 A054388 A054389 * A054391 A054392 A054393 KEYWORD nonn,look AUTHOR John W. Layman, May 09 2000 STATUS approved

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Last modified June 3 14:00 EDT 2023. Contains 363110 sequences. (Running on oeis4.)