

A245766


a(n) = 2*(n^2 + 1)  n*(1 + (1)^n).


2



2, 4, 6, 20, 26, 52, 62, 100, 114, 164, 182, 244, 266, 340, 366, 452, 482, 580, 614, 724, 762, 884, 926, 1060, 1106, 1252, 1302, 1460, 1514, 1684, 1742, 1924, 1986, 2180, 2246, 2452, 2522, 2740, 2814, 3044, 3122, 3364, 3446, 3700, 3786, 4052, 4142, 4420
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OFFSET

0,1


COMMENTS

Sum of the parts in the partitions of 2*n2 and 2*n+2 into two even parts, for n>0 (see example).


LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..10000
Index entries for sequences related to partitions
Index entries for linear recurrences with constant coefficients, signature (1,2,2,1,1).


FORMULA

G.f.: 2*(1 + x*(1 + x*(1 + x*(5 + 2*x)))) / ((1  x)^3*(1 + x)^2).
a(n) = a(n1) + 2*a(n2)  2*a(n3)  a(n4) + a(n5), n>4.
a(n) = (2n + 2)*floor((n + 1)/2) + (2n  2)*floor((n  1)/2).


EXAMPLE

a(1) = 4; there is no partition for 2(1)2 = 0, and for 2(1)+2 = 4, there is one partition into two even parts (2,2). The sum of these parts = 4.
a(3) = 20; 2(3)2 = 4 has one partition with two even parts (2,2). Also, 2(3)+2 = 8 has two partitions with two even parts: (6,2) and (4,4). The sum total of the parts in these partitions is 2 + 2 + 6 + 2 + 4 + 4 = 20.


MAPLE

A245766:=n>2*(n^2+1)  n*(1+(1)^n): seq(A245766(n), n=0..50);


MATHEMATICA

Table[2 (n^2 + 1)  n (1 + (1)^n), {n, 0, 50}]
CoefficientList[Series[2 (1 + x (1 + x (1 + x (5 + 2 x))))/((1  x)^3 (1 + x)^2), {x, 0, 50}], x]


PROG

(MAGMA) [2*(n^2+1)n*(1+(1)^n): n in [0..50]];
(PARI) vector(150, n, 2*((n1)^2+1)(n1)*(1(1)^n)) \\ Derek Orr, Jul 31 2014


CROSSREFS

Cf. A245764.
Sequence in context: A234019 A279188 A108439 * A193774 A241210 A176652
Adjacent sequences: A245763 A245764 A245765 * A245767 A245768 A245769


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Jul 31 2014


STATUS

approved



