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A207381 Total sum of the odd-indexed parts of all partitions of n. 4
1, 3, 7, 14, 25, 45, 72, 117, 180, 275, 403, 596, 846, 1206, 1681, 2335, 3183, 4342, 5820, 7799, 10321, 13622, 17798, 23221, 30009, 38706, 49567, 63316, 80366, 101805, 128211, 161134, 201537, 251495, 312508, 387535, 478674, 590072, 724920, 888795, 1086324 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For more information see A206563.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A066186(n) - A207382(n) = A066897(n) + A207382(n).

EXAMPLE

For n = 5, write the partitions of 5 and below write the sums of their odd-indexed parts:

.    5

.    3+2

.    4+1

.    2+2+1

.    3+1+1

.    2+1+1+1

.    1+1+1+1+1

.  ------------

.   20 + 4 + 1 = 25

The total sum of the odd-indexed parts is 25 so a(5) = 25.

MAPLE

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

      if n=0 then [1, 0$2]

    elif i<1 then [0$3]

    else g:= b(n, i-1); h:= `if`(i>n, [0$3], b(n-i, i));

         [g[1]+h[1], g[2]+h[3], g[3]+h[2]+i*h[1]]

      fi

    end:

a:= n-> b(n, n)[3]:

seq(a(n), n=1..50); # Alois P. Heinz, Mar 12 2012

MATHEMATICA

b[n_, i_] := b[n, i] = Module[{g, h}, If[n == 0 , {1, 0, 0}, If[i < 1, {0, 0, 0},  g = b[n, i - 1]; h = If[i > n, {0, 0, 0}, b[n - i, i]]; {g[[1]] + h[[1]], g[[2]] + h[[3]], g[[3]] + h[[2]] + i*h[[1]]}]]]; a[n_] := b[n, n][[3]]; Table [a[n], {n, 1, 50}] (* Jean-Fran├žois Alcover, Dec 09 2016 after Alois P. Heinz *)

CROSSREFS

Cf. A066186, A066897, A066898, A181187, A194714, A206283, A206563, A207031, A207032, A207382.

Sequence in context: A265252 A193911 A206417 * A008646 A036830 A014153

Adjacent sequences:  A207378 A207379 A207380 * A207382 A207383 A207384

KEYWORD

nonn

AUTHOR

Omar E. Pol, Feb 17 2012

EXTENSIONS

More terms from Alois P. Heinz, Mar 12 2012

STATUS

approved

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Last modified February 18 02:57 EST 2020. Contains 332006 sequences. (Running on oeis4.)