The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A319885 a(n) = 2*1 - 4*3 + 6*5 - 8*7 + 10*9 - 12*11 + 14*13 - 16*15 + ... - (up to the n-th term). 9
 2, 2, -2, -10, -4, 20, 12, -36, -26, 54, 42, -78, -64, 104, 88, -136, -118, 170, 150, -210, -188, 252, 228, -300, -274, 350, 322, -406, -376, 464, 432, -528, -494, 594, 558, -666, -628, 740, 700, -820, -778, 902, 858, -990, -944, 1080, 1032, -1176, -1126 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For similar sequences that alternate in descending blocks of k natural numbers, we have: a(n) = (-1)^floor(n/k) * Sum_{j=1..k-1} (floor((n-j)/k) - floor((n-j-1)/k)) * (Product_{i=1..j} n-i-j+k+1) + Sum_{j=1..n} (-1)^(floor(j/k)+1) * (floor(j/k) - floor((j-1)/k)) * (Product_{i=1..k} j-i+1). Here, k=2. The denominators of the generating functions for these sequences are (1 - x)*(1 + x^k)^(k+1). - Georg Fischer and Andrew Howroyd, Mar 07 2020 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,-3,3,-3,3,-1,1). FORMULA From Colin Barker, Oct 01 2018: (Start) G.f.: 2*x*(1 + x^2 - 4*x^3) / ((1 - x)*(1 + x^2)^3). a(n) = a(n-1) - 3*a(n-2) + 3*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6) + a(n-7) for n>7. (End) EXAMPLE a(1) = 2; a(2) = 2*1 = 2; a(3) = 2*1 - 4 = -2; a(4) = 2*1 - 4*3 = -10; a(5) = 2*1 - 4*3 + 6 = -4; a(6) = 2*1 - 4*3 + 6*5 = 20; a(7) = 2*1 - 4*3 + 6*5 - 8 = 12; a(8) = 2*1 - 4*3 + 6*5 - 8*7 = -36; a(9) = 2*1 - 4*3 + 6*5 - 8*7 + 10 = -26; a(10) = 2*1 - 4*3 + 6*5 - 8*7 + 10*9 = 54; a(11) = 2*1 - 4*3 + 6*5 - 8*7 + 10*9 - 12 = 42; a(12) = 2*1 - 4*3 + 6*5 - 8*7 + 10*9 - 12*11 = -78; a(13) = 2*1 - 4*3 + 6*5 - 8*7 + 10*9 - 12*11 + 14 = -64; a(14) = 2*1 - 4*3 + 6*5 - 8*7 + 10*9 - 12*11 + 14*13 = 104; a(15) = 2*1 - 4*3 + 6*5 - 8*7 + 10*9 - 12*11 + 14*13 - 16 = 88; a(16) = 2*1 - 4*3 + 6*5 - 8*7 + 10*9 - 12*11 + 14*13 - 16*15 = -136; a(17) = 2*1 - 4*3 + 6*5 - 8*7 + 10*9 - 12*11 + 14*13 - 16*15 + 18 = -118; a(18) = 2*1 - 4*3 + 6*5 - 8*7 + 10*9 - 12*11 + 14*13 - 16*15 + 18*17 = 170; etc. MAPLE a:=(n, k)->(-1)^(floor(n/k))* add((floor((n-j)/k)-floor((n-j-1)/k))*(mul(n-i-j+k+1, i=1..j)), j=1..k-1) + add( (-1)^(floor(j/k)+1)*(floor(j/k)-floor((j-1)/k))*(mul(j-i+1, i=1..k)), j=1..n): seq(a(n, 2), n=1..50); # Muniru A Asiru, Sep 30 2018 MATHEMATICA LinearRecurrence[{1, -3, 3, -3, 3, -1, 1}, {2, 2, -2, -10, -4, 20, 12}, 70] (* Harvey P. Dale, Mar 12 2023 *) PROG (PARI) Vec(2*x*(1 + x^2 - 4*x^3) / ((1 - x)*(1 + x^2)^3) + O(x^50)) \\ Colin Barker, Oct 01 2018 CROSSREFS For similar sequences, see: A001057 (k=1), this sequence (k=2), A319886 (k=3), A319887 (k=4), A319888 (k=5), A319889 (k=6), A319890 (k=7), A319891 (k=8), A319892 (k=9), A319893 (k=10). Sequence in context: A091185 A324956 A268081 * A368958 A125695 A152681 Adjacent sequences: A319882 A319883 A319884 * A319886 A319887 A319888 KEYWORD sign,easy AUTHOR Wesley Ivan Hurt, Sep 30 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 18 13:29 EDT 2024. Contains 371780 sequences. (Running on oeis4.)