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A206436 Total sum of even parts in the last section of the set of partitions of n. 2
0, 2, 0, 8, 2, 18, 10, 42, 28, 80, 70, 162, 148, 290, 300, 530, 562, 918, 1020, 1570, 1780, 2602, 3022, 4286, 4992, 6858, 8110, 10872, 12888, 16962, 20178, 26134, 31138, 39728, 47412, 59848, 71312, 89072, 106176, 131440, 156400, 192164, 228330, 278616, 330502 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also total sum of even parts in the n-th shell of the shell model of partitions.

Also total sum of even parts in the partitions of n that do not contain 1 as a part.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Alois P. Heinz)

FORMULA

G.f.: (Sum_{i>0} 2*i*x^(2*i)*(1-x)/(1-x^(2*i))) / Product_{i>0} (1-x^i). - Alois P. Heinz, Mar 16 2012

a(n) ~ Pi * exp(Pi*sqrt(2*n/3)) / (24*sqrt(2*n)). - Vaclav Kotesovec, May 29 2018

MAPLE

b:= proc(n, i) option remember; local g, h;

      if n=0 then [1, 0]

    elif i<1 then [0, 0]

    else g:= b(n, i-1); h:= `if`(i>n, [0, 0], b(n-i, i));

         [g[1]+h[1], g[2]+h[2] +((i+1) mod 2)*h[1]*i]

      fi

    end:

a:= n-> b(n, n)[2] -`if`(n=1, 0, b(n-1, n-1)[2]):

seq(a(n), n=1..60);  # Alois P. Heinz, Mar 16 2012

MATHEMATICA

b[n_, i_] := b[n, i] = Module[{g, h}, Which[n == 0, {1, 0}, i < 1, {0, 0}, True, g = b[n, i-1]; h = If[i>n, {0, 0}, b[n-i, i]]; {g[[1]] + h[[1]], g[[2]] + h[[2]] + Mod[i+1, 2]*h[[1]]*i}]]; a[n_] := b[n, n][[2]] - If[n == 1, 0, b[n-1, n-1][[2]]]; Table[a[n], {n, 1, 60}] (* Jean-Fran├žois Alcover, Feb 16 2017, after Alois P. Heinz *)

CROSSREFS

Partial sums give A066966.

Cf. A135010, A138121, A138879.

Sequence in context: A199268 A268499 A298522 * A146543 A179990 A228156

Adjacent sequences:  A206433 A206434 A206435 * A206437 A206438 A206439

KEYWORD

nonn

AUTHOR

Omar E. Pol, Feb 12 2012

EXTENSIONS

More terms from Alois P. Heinz, Mar 16 2012

STATUS

approved

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)