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A296805 Sum of the larger parts in the partitions of n into two distinct parts with the larger part even. 1
0, 0, 2, 0, 4, 4, 10, 6, 14, 14, 24, 18, 30, 30, 44, 36, 52, 52, 70, 60, 80, 80, 102, 90, 114, 114, 140, 126, 154, 154, 184, 168, 200, 200, 234, 216, 252, 252, 290, 270, 310, 310, 352, 330, 374, 374, 420, 396, 444, 444, 494, 468, 520, 520, 574, 546, 602, 602 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for sequences related to partitions

Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-2,0,0,-1,1).

FORMULA

a(n) = Sum_{i=1..floor((n-1)/2)} (n-i) * ((n-i+1) mod 2).

G.f.: 2*x^3*(1-x+2*x^2+x^4)/((1-x)*(1-x^4)^2). - Robert Israel, Dec 20 2017

EXAMPLE

a(12) = 18; the partitions of 12 into two distinct parts are (11,1), (10,2), (9,3), (8,4) and (7,5). The sum of the even numbers among the larger parts gives 10 + 8 = 18.

MAPLE

f:= gfun:-rectoproc({a(n-9)-a(n-8)-2*a(n-5)+2*a(n-4)+a(n-1)-a(n)=0, seq(a(n)=[0, 0, 2, 0, 4, 4, 10, 6, 14][n], n=1..9)}, a(n), remember):

map(f, [$1..100]); # Robert Israel, Dec 21 2017

MATHEMATICA

Table[Sum[(n - i)  Mod[n - i + 1, 2], {i, Floor[(n - 1)/2]}], {n, 80}]

CROSSREFS

Sequence in context: A147980 A021493 A195395 * A084247 A300307 A286606

Adjacent sequences:  A296802 A296803 A296804 * A296806 A296807 A296808

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Dec 20 2017

STATUS

approved

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Last modified November 18 07:55 EST 2018. Contains 317279 sequences. (Running on oeis4.)