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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Sum of the parts in the partitions of 2*n-2 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 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(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5), 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*((n-1)^2+1)-(n-1)*(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

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Last modified December 8 02:30 EST 2019. Contains 329850 sequences. (Running on oeis4.)