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 A171426 Row sum of column n in A126441 or A161924. 2
 1, 5, 16, 49, 129, 341, 833, 2029, 4760, 11068, 25182, 56888, 126661, 280169, 613893, 1337386, 2893793, 6232013, 13352607, 28497552, 60580905, 128368080, 271153740, 571224871, 1200298631, 2516483260, 5264785310, 10993631034, 22915508186, 47688470005 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Emeric Deutsch, Sep 06 2017: (Start) Row sums of the triangle A161919. a(n) = sum of the viabin numbers of the partitions of n. The viabin number of an integer partition is defined in the following way. Consider the southeast border of the Ferrers board of the integer partition and consider the binary number obtained by replacing each east step with 1 and each north step, except the last one, with 0. The corresponding decimal form is, by definition, the viabin number of the given integer partition. "Viabin" is coined from "via binary". For example, consider the integer partition [3,1,1] of 5. The southeast border of its Ferrers board yields 10011, leading to the viabin number 19. (End) LINKS Alois P. Heinz, Table of n, a(n) for n = 1..60 EXAMPLE The values 8,9,6,11,15 map to 1111,211,22,31,4, respectively; so a(4) = 8+9+6+11+15 = 49. MAPLE with(combinat): a := proc (n) local ff, partovi: ff := proc (X) local s: s := [1, seq(0, j = 1 .. X)]: s := map(convert, s, string): return cat(op(s)) end proc: partovi := proc (P) local X, n, Y, i: X := convert(P, multiset): n := X[-1]: Y := map(proc (t) options operator, arrow: t end proc, X): for i to n do if member(i, Y) = false then X := [op(X), [i, 0]] end if end do: X := sort(X, proc (s, t) options operator, arrow: evalb(s < t) end proc): X := map(ff, X); X := cat(op(X)): n := parse(X): n := convert(n, decimal, binary): (1/2)*n end proc: add(partovi(partition(n)[j]), j = 1 .. numbpart(n)) end proc: seq(a(n), n = 1 .. 27); # the subprogram partovi (due to W. Edwin Clark) yields the viabin number of a given partition. # Emeric Deutsch, Sep 06 2017 # second Maple program: b:= proc(n, i, l, r) option remember; `if`(n=0, r, `if`(i>n, 0,       b(n, i+1, l, r)+b(n-i, i\$2, ((x-> 2*x+1)@@(i-l))(2*r))))     end: a:= n-> b(n, 1, 0\$2): seq(a(n), n=1..30);  # Alois P. Heinz, Mar 01 2021 MATHEMATICA b[n_, i_, l_, r_] := b[n, i, l, r] = If[n == 0, r, If[i>n, 0,      b[n, i+1, l, r] + b[n-i, i, i, Nest[2#+1&, 2r, i-l]]]]; a[n_] := b[n, 1, 0, 0]; Array[a, 30] (* Jean-François Alcover, Mar 02 2021, after Alois P. Heinz *) CROSSREFS Cf. A161924, A171429. Sequence in context: A197201 A166868 A055144 * A180129 A244410 A052909 Adjacent sequences:  A171423 A171424 A171425 * A171427 A171428 A171429 KEYWORD easy,nonn AUTHOR Alford Arnold, Dec 12 2009 EXTENSIONS Ninth term corrected by Alford Arnold, Jan 22 2010 Offset changed to 1 and a(17)-a(27) from Emeric Deutsch, Sep 06 2017 a(28)-a(30) from Alois P. Heinz, Sep 07 2017 STATUS approved

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Last modified April 11 08:10 EDT 2021. Contains 342886 sequences. (Running on oeis4.)