A089594 -id:A089594 - cp's OEIS frontend

A130472 A permutation of the integers: a(n) = (-1)^n * floor( (n+1)/2 ).

0, -1, 1, -2, 2, -3, 3, -4, 4, -5, 5, -6, 6, -7, 7, -8, 8, -9, 9, -10, 10, -11, 11, -12, 12, -13, 13, -14, 14, -15, 15, -16, 16, -17, 17, -18, 18, -19, 19, -20, 20, -21, 21, -22, 22, -23, 23, -24, 24, -25, 25, -26, 26, -27, 27, -28, 28, -29, 29, -30, 30, -31, 31, -32, 32

Offset: 0

Clark Kimberling, May 28 2007

Pisano period lengths: 1, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, ... - R. J. Mathar, Aug 10 2012

Partial sums of A038608. - Stanislav Sykora, Nov 27 2013

G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (-1,1,1).
Index entries for sequences that are permutations of the integers

Sums of the form Sum_{k=0..n} k^p * q^k: A059841 (p=0,q=-1), this sequence (p=1,q=-1), A089594 (p=2,q=-1), A232599 (p=3,q=-1), A126646 (p=0,q=2), A036799 (p=1,q=2), A036800 (p=2,q=2), A036827 (p=3,q=2), A077925 (p=0,q=-2), A232600 (p=1,q=-2), A232601 (p=2,q=-2), A232602 (p=3,q=-2), A232603 (p=2,q=-1/2), A232604 (p=3,q=-1/2).

Cf. A001057, A038608.

[((-1)^n*(2*n+1)-1)/4: n in [0..80]]; // Vincenzo Librandi, Mar 29 2015

A130472:=n->ceil(n/2)*(-1)^n; seq(A130472(k), k=0..50); # Wesley Ivan Hurt, Oct 22 2013

CoefficientList[Series[(x^2-x)/(1-x^2)^2, {x, 0, 64}], x] (* Geoffrey Critzer, Sep 29 2013 *)
LinearRecurrence[{-1,1,1},{0,-1,1},70] (* Harvey P. Dale, Mar 02 2018 *)

a(n)=(-1)^n*n\2 \\ Charles R Greathouse IV, Sep 02 2015

[((-1)^n*(2*n+1) - 1)/4 for n in (0..70)] # G. C. Greubel, Mar 31 2021

a(n) = -A001057(n).
a(2n) = n, a(2n+1) = -(n+1).
a(n) = Sum_{k=0..n} k*(-1)^k.
a(n) = -a(n-1) +a(n-2) +a(n-3).
G.f.: -x/( (1-x)*(1+x)^2 ). - R. J. Mathar, Feb 20 2011
a(n) = floor( (n/2)*(-1)^n ). - Wesley Ivan Hurt, Jun 14 2013
a(n) = ceiling( n/2 )*(-1)^n. - Wesley Ivan Hurt, Oct 22 2013
a(n) = ((-1)^n*(2*n+1) - 1)/4. - Adriano Caroli, Mar 28 2015
E.g.f.: (1/4)*(-exp(x) + (1-2*x)*exp(-x) ). - G. C. Greubel, Mar 31 2021

A232599 Alternating sum of cubes, i.e., Sum_{k=0..n} k^p*q^k for p=3, q=-1.

Original entry on oeis.org

0, -1, 7, -20, 44, -81, 135, -208, 304, -425, 575, -756, 972, -1225, 1519, -1856, 2240, -2673, 3159, -3700, 4300, -4961, 5687, -6480, 7344, -8281, 9295, -10388, 11564, -12825, 14175, -15616, 17152, -18785, 20519

Offset: 0

Stanislav Sykora, Nov 26 2013

			a(3) = 0^3 - 1^3 + 2^3 - 3^3 = -20.

Stanislav Sykora, Table of n, a(n) for n = 0..1000
S. Sykora, Finite and Infinite Sums of the Power Series (k^p)(x^k), DOI 10.3247/SL1Math06.002, Section V.
Index entries for linear recurrences with constant coefficients, signature (-3,-2,2,3,1).

Cf. A000578 (cubes), A011934 (absolute values), A059841 (p=0,q=-1), A130472 (p=1,q=-1), A089594 (p=2,q=-1), A126646 (p=0,q=2), A036799 (p=1,q=2), A036800 (p=2,q=2), A036827 (p=3,q=2), A077925 (p=0,q=-2), A232600 (p=1,q=-2), A232601 (p=2,q=-2), A232602 (p=3,q=-2), A232603 (p=2,q=-1/2), A232604 (p=3,q=-1/2).

[(1 - (-1)^n*(1 -6*n^2 -4*n^3))/8: n in [0..30]]; // G. C. Greubel, Mar 31 2021

A232599:= n-> (1 -(-1)^n*(1 -6*n^2 -4*n^3))/8; seq(A232599(n), n=0..30); # G. C. Greubel, Mar 31 2021

Accumulate[Times@@@Partition[Riffle[Range[0,40]^3,{1,-1},{2,-1,2}],2]] (* Harvey P. Dale, Jul 22 2016 *)

S3M1(n)=((-1)^n*(4*n^3+6*n^2-1)+1)/8;
v = vector(10001);for(k=1,#v,v[k]=S3M1(k-1))

[(1 - (-1)^n*(1 -6*n^2 -4*n^3))/8 for n in (0..30)] # G. C. Greubel, Mar 31 2021

a(n) = ((-1)^n*(4*n^3+6*n^2-1) +1)/8.
G.f.: (-x)*(1-4*x+x^2) / ( (1-x)*(1+x)^4 ). - R. J. Mathar, Nov 23 2014
E.g.f.: (exp(x) - (1 +10*x -18*x^2 +4*x^3)*exp(-x))/8. - G. C. Greubel, Mar 31 2021
a(n) = - 3*a(n-1) - 2*a(n-2) + 2*a(n-3) + 3*a(n-4) + a(n-5). - Wesley Ivan Hurt, Mar 31 2021

A232600 a(n) = Sum_{k=0..n} k^p*q^k, where p=1, q=-2.

Original entry on oeis.org

0, -2, 6, -18, 46, -114, 270, -626, 1422, -3186, 7054, -15474, 33678, -72818, 156558, -334962, 713614, -1514610, 3203982, -6757490, 14214030, -29826162, 62448526, -130489458, 272163726, -566697074, 1178133390, -2445745266, 5070447502, -10498808946, 21713445774

Offset: 0

Stanislav Sykora, Nov 27 2013

			a(3) = 0^1*2^0 - 1^1*2^1 + 2^1*2^2 - 3^1*2^3 = -18.

Stanislav Sykora, Table of n, a(n) for n = 0..1000
S. Sykora, Finite and Infinite Sums of the Power Series (k^p)(x^k), DOI 10.3247/SL1Math06.002, Section V.
Index entries for linear recurrences with constant coefficients, signature (-3,0,4).

Cf. A045883, A140960 (absolute values), A059841 (p=0, q=-1), A130472 (p=1 ,q=-1), A089594 (p=2, q=-1), A232599 (p=3, q=-1), A126646 (p=0, q=2), A036799 (p=1, q=2), A036800 (p=q=2), A036827 (p=3, q=2), A077925 (p=0, q=-2), A232601 (p=2, q=-2), A232602 (p=3, q=-2), A232603 (p=2, q=-1/2), A232604 (p=3, q=-1/2).

Cf. A045883.

[2*((-2)^n*(3*n+1) -1)/9: n in [0..30]]; // G. C. Greubel, Mar 31 2021

A232600:= n-> 2*((-2)^n*(3*n+1) -1)/9; seq(A232600(n), n=0..30); # G. C. Greubel, Mar 31 2021

Table[2((3n+1)(-2)^n -1)/9, {n, 0, 30}] (* Bruno Berselli, Nov 28 2013 *)

PARI
```
a(n)=-((3*n+1)*(-2)^(n+1)+2)/9;
```

[2*((-2)^n*(3*n+1) -1)/9 for n in (0..30)] # G. C. Greubel, Mar 31 2021

a(n) = 2*( (3*n+1)*(-2)^n - 1 )/9.
abs(a(n)) = 2*A045883(n) = A140960(n).
From Bruno Berselli, Nov 28 2013: (Start)
G.f.: -2*x / ((1 - x)*(1 + 2*x)^2). [corrected by Georg Fischer, May 11 2019]
a(n) = -3*a(n-1) +4*a(n-3). (End)
From G. C. Greubel, Mar 31 2021: (Start)
E.g.f.: (2/9)*(-exp(x) + (1-6*x)*exp(-2*x)).
a(n) = 2*(-1)^n*A045883(n). (End)

A232601 a(n) = Sum_{k=0..n} k^p*q^k for p = 2 and q = -2.

Original entry on oeis.org

0, -2, 14, -58, 198, -602, 1702, -4570, 11814, -29658, 72742, -175066, 414758, -969690, 2241574, -5131226, 11645990, -26233818, 58700838, -130567130, 288863270, -635980762, 1394062374, -3043511258, 6620165158

Offset: 0

Stanislav Sykora, Nov 27 2013

			a(3) = 0^2*2^0 - 1^2*2^1 + 2^2*2^2 - 3^2*2^3 = -58.

Stanislav Sykora, Table of n, a(n) for n = 0..1000
Stanislav Sykora, Finite and Infinite Sums of the Power Series (k^p)(x^k), DOI 10.3247/SL1Math06.002, Section V.
Index entries for linear recurrences with constant coefficients, signature (-5,-6,4,8).

Cf. A059841 (p=0,q=-1), A130472 (p=1,q=-1), A089594 (p=2,q=-1), A232599 (p=3,q=-1), A126646 (p=0,q=2), A036799 (p=1,q=2), A036800 (p=2,q=2), A036827 (p=3,q=2), A077925 (p=0,q=-2), A232600 (p=1,q=-2), A232602 (p=3,q=-2), A232603 (p=2,q=-1/2), A232604 (p=3,q=-1/2).

[2*(1 - (-2)^n*(1-6*n-9*n^2))/27: n in [0..30]]; // G. C. Greubel, Mar 31 2021

A232601:= n-> 2*(1 - (-2)^n*(1-6*n-9*n^2))/27; seq(A232601(n), n=0..30); # G. C. Greubel, Mar 31 2021

LinearRecurrence[{-5,-6,4,8},{0,-2,14,-58},30] (* Harvey P. Dale, Aug 20 2015 *)

S2M2(n)=((-1)^n*2^(n+1)*(9*n^2+6*n-1)+2)/27;
v = vector(10001); for(k=1, #v, v[k]=S2M2(k-1))

[2*(1 - (-2)^n*(1-6*n-9*n^2))/27 for n in (0..30)] # G. C. Greubel, Mar 31 2021

a(n) = 2*((-2)^n * (9*n^2 + 6*n - 1) + 1)/27.
G.f.: 2*x*(-1 + 2*x) / ((1-x)*(1+2*x)^3). - R. J. Mathar, Nov 23 2014
E.g.f.: (2/27)*(exp(x) - (1 +30*x -36*x^2)*exp(-2*x)). - G. C. Greubel, Mar 31 2021
a(n) = - 5*a(n-1) - 6*a(n-2) + 4*a(n-3) + 8*a(n-4). - Wesley Ivan Hurt, Mar 31 2021

A232602 a(n) = Sum_{k=0..n} k^p*q^k, where p=3, q=-2.

Original entry on oeis.org

0, -2, 30, -186, 838, -3162, 10662, -33242, 97830, -275418, 748582, -1977306, 5100582, -12897242, 32060454, -78531546, 189903910, -454052826, 1074770982, -2521320410, 5867287590, -13554437082

Offset: 0

Stanislav Sykora, Nov 27 2013

			a(3) = 0^3*2^0 - 1^3*2^1 + 2^3*2^2 - 3^3*2^3 = -186.

Stanislav Sykora, Table of n, a(n) for n = 0..1000
S. Sykora, Finite and Infinite Sums of the Power Series (k^p)(x^k), DOI 10.3247/SL1Math06.002, Section V.
Index entries for linear recurrences with constant coefficients, signature (-7,-16,-8,16,16).

Cf. A059841 (p=0,q=-1), A130472 (p=1,q=-1), A089594 (p=2,q=-1), A232599 (p=3,q=-1), A126646 (p=0,q=2), A036799 (p=1,q=2), A036800 (p=2,q=2), A036827 (p=3,q=2), A077925 (p=0,q=-2), A232600 (p=1,q=-2), A232601 (p=2,q=-2), A232603 (p=2,q=-1/2), A232604 (p=3,q=-1/2).

[2*(1 -(-2)^n*(1 +3*n -9*n^2 -9*n^3))/27: n in [0..35]]; // G. C. Greubel, Mar 31 2021

A232602:= n-> 2*(1 -(-2)^n*(1 +3*n -9*n^2 -9*n^3))/27; seq(A232602(n), n=0..35); # G. C. Greubel, Mar 31 2021

LinearRecurrence[{-7,-16,-8,16,16}, {0,-2,30,-186,838}, 40] (* G. C. Greubel, Mar 31 2021 *)

a(n)=((-1)^n*2^(n+1)*(27*n^3+27*n^2-9*n-3)+6)/81;

[2*(1 -(-2)^n*(1 +3*n -9*n^2 -9*n^3))/27 for n in (0..35)] # G. C. Greubel, Mar 31 2021

a(n) = 2*(1 - (-2)^n*(1 +3*n -9*n^2 -9*n^3))/27.
G.f.: -2*x*(1-8*x+4*x^2) / ( (1-x)*(1+2*x)^4 ). - R. J. Mathar, Nov 23 2014
E.g.f.: (2/27)*(exp(x) - (1 +30*x -144*x^2 +72*x^3)*exp(-2*x)). - G. C. Greubel, Mar 31 2021
a(n) = - 7*a(n-1) - 16*a(n-2) - 8*a(n-3) + 16*a(n-4) + 16*a(n-5). - Wesley Ivan Hurt, Mar 31 2021

A036827 a(n) = 26 + 2^(n+1)(-13 +9n -3*n^2 +n^3).

Original entry on oeis.org

0, 2, 34, 250, 1274, 5274, 19098, 63002, 194074, 567322, 1591322, 4317210, 11395098, 29392922, 74350618, 184942618, 453378074, 1097334810, 2626158618, 6222250010, 14610858010, 34032582682, 78693531674, 180757725210, 412685959194

Offset: 0

N. J. A. Sloane

			a(3) = 2^0*0^3 + 2^1*1^3 + 2^2*2^3 + 2^3*3^3 = 250.

M. Petkovsek et al., A=B, Peters, 1996, p. 97.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
S. Sykora, Finite and Infinite Sums of the Power Series (k^p)(x^k), DOI 10.3247/SL1Math06.002, Section V.
Index entries for linear recurrences with constant coefficients, signature (9,-32,56,-48,16).

Cf. A059841 (p=0,q=-1), A130472 (p=1,q=-1), A089594 (p=2,q=-1), A232599 (p=3,q=-1), A126646 (p=0,q=2), A036799 (p=1,q=2), A036800 (p=2,q=2), this sequence (p=3,q=2), A077925 (p=0,q=-2), A232600 (p=1,q=-2), A232601 (p=2,q=-2), A232602 (p=3,q=-2), A232603 (p=2,q=-1/2), A232604 (p=3,q=-1/2).

a036827 n = 2^(n+1) * (n^3 - 3*n^2 + 9*n - 13) + 26
-- Reinhard Zumkeller, May 24 2012

[2*(13 + 2^n*(-13 +9*n -3*n^2 +n^3)): n in [0..35]]; // G. C. Greubel, Mar 31 2021

A036827:= n-> 2*(13 + 2^n*(-13 +9*n -3*n^2 +n^3)); seq(A026827(n), n=0..30); # G. C. Greubel, Mar 31 2021

Table[26 +2^(n+1)(-13 +9n -3n^2 +n^3), {n, 0, 30}] (* or *) LinearRecurrence[ {9, -32, 56, -48, 16}, {0, 2, 34, 250, 1274}, 31] (* Harvey P. Dale, Dec 15 2011 *)

a(n)=26+2^(n+1)*(-13+9*n-3*n^2+n^3) \\ Charles R Greathouse IV, Oct 07 2015

[2*(13 + 2^n*(-13 +9*n -3*n^2 +n^3)) for n in (0..35)] # G. C. Greubel, Mar 31 2021

a(n) = Sum_{k=0..n} 2^k*k^3. - Benoit Cloitre, Jun 11 2003
G.f.: 2*x*(1 +8*x +4*x^2)/((1-x)*(1-2*x)^4). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009
a(n) = 9*a(n-1) -32*a(n-2) +56*a(n-3) -48*a(n-4) +16*a(n-5) for n>4 with a(0)=0, a(1)=2, a(2)=34, a(3)=250, a(4)=1274. - Harvey P. Dale, Dec 15 2011
a(n) = Sum_{k=0..n} Sum_{i=0..n} k^3 * C(k,i). - Wesley Ivan Hurt, Sep 21 2017
E.g.f.: 2 (13*exp(x) + (-13 +14*x +8*x^3)*exp(2*x)). - G. C. Greubel, Mar 31 2021

A225144 a(n) = Sum_{i=n..2n} i^2(-1)^i.

Original entry on oeis.org

0, 3, 11, 18, 42, 45, 93, 84, 164, 135, 255, 198, 366, 273, 497, 360, 648, 459, 819, 570, 1010, 693, 1221, 828, 1452, 975, 1703, 1134, 1974, 1305, 2265, 1488, 2576, 1683, 2907, 1890, 3258, 2109, 3629, 2340, 4020, 2583, 4431, 2838, 4862, 3105, 5313, 3384

Offset: 0

Bruno Berselli, Jun 06 2013

3 and 11 are the only primes in the sequence.

			a(6) = 6^2-7^2+8^2-9^2+10^2-11^2+12^2 = 93.
a(7) = -7^2+8^2-9^2+10^2-11^2+12^2-13^2+14^2 = 84.

Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Cf. A050409: sum(i^2, i=n..2n); A064455: sum(i*(-1)^i, i=n..2n); A065679: A000217(n)+(-1)^n*A000217(n-1); A089594: sum(i^2*(-1)^i, i=1..n).

[&+[i^2*(-1)^i: i in [n..2*n]]: n in [0..50]];

Table[Sum[i^2 (-1)^i, {i, n, 2 n}], {n, 0, 50}]

G.f.: x*(3+11*x+9*x^2+9*x^3)/(1-x^2)^3.
a(n) = 3*a(n-2)-3*a(n-4)+a(n-6).
a(n) = n*(4*n+(n-1)*(-1)^n+2)/2.
a(n) = A000217(2n) +(-1)^n*A000217(n-1) with A000217(-1)=0.
a(2n-1) = A094159(n) for n>0; a(2n) = A055437(n) for A055437(0)=0.

A266085 Alternating sum of heptagonal numbers.

Original entry on oeis.org

0, -1, 6, -12, 22, -33, 48, -64, 84, -105, 130, -156, 186, -217, 252, -288, 328, -369, 414, -460, 510, -561, 616, -672, 732, -793, 858, -924, 994, -1065, 1140, -1216, 1296, -1377, 1462, -1548, 1638, -1729, 1824, -1920, 2020, -2121, 2226, -2332, 2442, -2553

Offset: 0

Ilya Gutkovskiy, Dec 21 2015

G. C. Greubel, Table of n, a(n) for n = 0..5000
OEIS Wiki, Figurate numbers
Eric Weisstein's World of Mathematics, Heptagonal Number
Index entries for linear recurrences with constant coefficients, signature (-2,0,2,1).

Cf. A000566, A002413, A006578, A008728, A035608, A083392, A089594.

Unsigned terms give antidiagonal sums of A204154. - Nathaniel J. Strout, Nov 14 2019

[((10*n^2+4*n-3)*(-1)^n+3)/8: n in [0..50]]; // Vincenzo Librandi, Dec 21 2015

R:=PowerSeriesRing(Integers(), 50); [0] cat  Coefficients(R!(-x*(1 - 4*x)/((1 - x)*(1 + x)^3))); // Marius A. Burtea, Nov 13 2019

Table[((10 n^2 + 4 n - 3) (-1)^n + 3)/8, {n, 0, 50}]
CoefficientList[Series[(x - 4 x^2)/(x^4 + 2 x^3 - 2 x - 1), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 21 2015 *)
LinearRecurrence[{-2,0,2,1},{0,-1,6,-12},60] (* Harvey P. Dale, Jan 26 2023 *)

x='x+O('x^100); concat(0, Vec(-x*(1-4*x)/((1-x)*(1+x)^3))) \\ Altug Alkan, Dec 21 2015

G.f.: -x*(1 - 4*x)/((1 - x)*(1 + x)^3).
a(n) = ((10*n^2 + 4*n - 3)*(-1)^n + 3)/8.
a(n) = Sum_{k = 0..n} (-1)^k*A000566(k).
Lim_{n -> infinity} a(n + 1)/a(n) = -1.
a(n) = (-1)^n*A008728(5*n-5) for n>0. - Bruno Berselli, Dec 21 2015
E.g.f.: (1/8)*exp(-x)*(-3 + 3*exp(2*x) - 14*x + 10*x^2). - Stefano Spezia, Nov 13 2019

A261032 a(n) = (-1)^n(n^8 + 4n^7 - 14n^5 + 28n^3 - 17*n)/2.

Original entry on oeis.org

0, -1, 255, -6306, 59230, -331395, 1348221, -4416580, 12360636, -30686085, 69313915, -145044966, 284936730, -530793991, 944995065, -1617895560, 2677071736, -4298685705, 6721274871, -10262288170, 15337711830, -22485147531, 32390726005, -45920259276, 64155054900, -88432835725

Offset: 0

Ilya Gutkovskiy, Nov 18 2015

Alternating sum of eighth powers (A001016).

For n>0, a(n) is divisible by A000217(n).

			a(0) = 0^8 = 0,
a(1) = 0^8 -1^8 = -1,
a(2) = 0^8 -1^8 + 2^8 = 255,
a(3) = 0^8 -1^8 + 2^8 - 3^8 = -6306,
a(4) = 0^8 -1^8 + 2^8 - 3^8 + 4^8 = 59230,
a(5) = 0^8 -1^8 + 2^8 - 3^8 + 4^8 - 5^8 = -331395, etc.

Robert Israel, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (-9,-36,-84,-126,-126,-84,-36,-9,-1 ).

Cf. A000217, A001016, A000542, A089594, A232599, A062392, A062393, A152725, A152726.

[(-1)^n*(n^8+4*n^7-14*n^5+28*n^3-17*n)/2: n in [0..30]]; // Vincenzo Librandi, Nov 20 2015

seq((-1)^n*(n^8 + 4*n^7 - 14*n^5 + 28*n^3 - 17*n)/2, n = 0 .. 100); # Robert Israel, Nov 18 2015

Table[(1/2) (-1)^n n (n + 1) (n^6 + 3 n^5 - 3 n^4 - 11 n^3 + 11 n^2 + 17 n - 17), {n, 0, 25}]

vector(100, n, n--; (-1)^n*(n^8+4*n^7-14*n^5+28*n^3-17*n)/2) \\ Altug Alkan, Nov 18 2015

[(-1)^n*(n^8 +4*n^7 -14*n^5 +28*n^3 -17*n)/2 for n in (0..40)] # G. C. Greubel, Apr 02 2021

G.f.: -x*(1 - 246*x + 4047*x^2 - 11572*x^3 + 4047*x^4 - 246*x^5 + x^6)/(1 + x)^9.
a(n) = Sum_{k = 0..n} (-1)^k*k^8.
a(n) = (-1)^n*n*(n + 1)*(n^6 + 3*n^5 - 3*n^4 - 11*n^3 + 11*n^2 + 17*n - 17)/2.
Sum_{n>0} 1/a(n) = -0.9962225712723456482...
Sum_{j=0..9} binomial(9,j)*a(n-j) = 0. - Robert Israel, Nov 18 2015
E.g.f.: (x/2)*(-2 +253*x -1848*x^2 +2961*x^3 -1596*x^4 +350*x^5 -32*x^6 +x^7)*exp(-x). - G. C. Greubel, Apr 02 2021

A266086 Alternating sum of 9-gonal (or nonagonal) numbers.

Original entry on oeis.org

0, -1, 8, -16, 30, -45, 66, -88, 116, -145, 180, -216, 258, -301, 350, -400, 456, -513, 576, -640, 710, -781, 858, -936, 1020, -1105, 1196, -1288, 1386, -1485, 1590, -1696, 1808, -1921, 2040, -2160, 2286, -2413, 2546, -2680, 2820, -2961, 3108, -3256, 3410

Offset: 0

Ilya Gutkovskiy, Dec 21 2015

G. C. Greubel, Table of n, a(n) for n = 0..5000
OEIS Wiki, Figurate numbers
Eric Weisstein's World of Mathematics, Nonagonal Number
Index entries for linear recurrences with constant coefficients, signature (-2,0,2,1).

Cf. A001106, A006578, A007584, A035608, A083392, A089594.

[(14*(-1)^n*n^2 + 4*(-1)^n*n - 5*(-1)^n + 5)/8: n in [0..50]]; // Vincenzo Librandi, Dec 21 2015

Table[((14 n^2 + 4 n - 5) (-1)^n + 5)/8, {n, 0, 44}]
CoefficientList[Series[(x - 6 x^2)/(x^4 + 2 x^3 - 2 x - 1), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 21 2015 *)

x='x+O('x^100); concat(0, Vec(-x*(1-6*x)/((1-x)*(1+x)^3))) \\ Altug Alkan, Dec 21 2015

G.f.: -x*(1 - 6*x)/((1 - x)*(1 + x)^3).
a(n) = ((14*n^2 + 4*n - 5)*(-1)^n + 5)/8.
a(n) = Sum_{k = 0..n} (-1)^k*A001106(k).
Lim_{n -> infinity} a(n + 1)/a(n) = -1.

cp's OEIS Frontend

A130472 A permutation of the integers: a(n) = (-1)^n * floor( (n+1)/2 ).

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A232599 Alternating sum of cubes, i.e., Sum_{k=0..n} k^p*q^k for p=3, q=-1.

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A232600 a(n) = Sum_{k=0..n} k^p*q^k, where p=1, q=-2.

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A232601 a(n) = Sum_{k=0..n} k^p*q^k for p = 2 and q = -2.

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A232602 a(n) = Sum_{k=0..n} k^p*q^k, where p=3, q=-2.

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A036827 a(n) = 26 + 2^(n+1)*(-13 +9*n -3*n^2 +n^3).

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A036827 a(n) = 26 + 2^(n+1)(-13 +9n -3*n^2 +n^3).

A225144 a(n) = Sum_{i=n..2n} i^2(-1)^i.

A261032 a(n) = (-1)^n(n^8 + 4n^7 - 14n^5 + 28n^3 - 17*n)/2.