A374010 -id:A374010 - cp's OEIS frontend

A131179 a(n) = if n mod 2 == 0 then n(n+1)/2, otherwise (n-1)n/2 + 1.

0, 1, 3, 4, 10, 11, 21, 22, 36, 37, 55, 56, 78, 79, 105, 106, 136, 137, 171, 172, 210, 211, 253, 254, 300, 301, 351, 352, 406, 407, 465, 466, 528, 529, 595, 596, 666, 667, 741, 742, 820, 821, 903, 904, 990, 991, 1081, 1082, 1176, 1177, 1275, 1276, 1378, 1379, 1485

Offset: 0

Philippe LALLOUET, Sep 16 2007

From Wesley Ivan Hurt, Jun 24 2024: (Start)
Fill an array with the natural numbers n = 1,2,... along diagonals in alternating 'down' and 'up' directions. For n > 0, a(n) is row 1 of the boustrophedon-style array (see example).
In general, row k is given by (1+t^2+(n-k)*(-1)^t)/2, t = n+k-1. Here, k=1, n>0. (End)

			       [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9] [10] [11] [12]
  [ 1]   1    3    4   10   11   21   22   36   37   55   56   78   ...
  [ 2]   2    5    9   12   20   23   35   38   54   57   77   ...
  [ 3]   6    8   13   19   24   34   39   53   58   76   ...
  [ 4]   7   14   18   25   33   40   52   59   75   ...
  [ 5]  15   17   26   32   41   51   60   74   ...
  [ 6]  16   27   31   42   50   61   73   ...
  [ 7]  28   30   43   49   62   72   ...
  [ 8]  29   44   48   63   71   ...
  [ 9]  45   47   64   70   ...
  [10]  46   65   69   ...
  [11]  66   68   ...
  [12]  67   ...
        ...
- _Wesley Ivan Hurt_, Jun 24 2024

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Cf. A128918.

For rows k = 1..10: this sequence (k=1) n>0, A373662 (k=2), A373663 (k=3), A374004 (k=4), A374005 (k=5), A374007 (k=6), A374008 (k=7), A374009 (k=8), A374010 (k=9), A374011 (k=10).

a131179 n = (n + 1 - m) * n' + m  where (n', m) = divMod n 2
-- Reinhard Zumkeller, Oct 12 2013

[(n^2+1+(n-1)*(-1)^n )/2: n in [0..60]]; // Vincenzo Librandi, Feb 12 2016

LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 3, 4, 10}, 60] (* Jean-François Alcover, Feb 12 2016 *)
Table[If[EvenQ[n],(n(n+1))/2,(n(n-1))/2+1],{n,0,60}] (* Harvey P. Dale, Jul 25 2024 *)

def A131179(n): return n*(n+1)//2 + (1-n)*(n % 2) # Chai Wah Wu, May 24 2022

G.f.: -x*(1+2*x-x^2+2*x^3)/((1+x)^2*(x-1)^3). - R. J. Mathar, Sep 05 2012

a(n) = ( n^2+1+(n-1)*(-1)^n )/2. - Luce ETIENNE, Aug 19 2014

A373662 a(n) = (1 + (n+1)^2 - (n-2)*(-1)^n)/2.

Original entry on oeis.org

2, 5, 9, 12, 20, 23, 35, 38, 54, 57, 77, 80, 104, 107, 135, 138, 170, 173, 209, 212, 252, 255, 299, 302, 350, 353, 405, 408, 464, 467, 527, 530, 594, 597, 665, 668, 740, 743, 819, 822, 902, 905, 989, 992, 1080, 1083, 1175, 1178, 1274, 1277, 1377, 1380, 1484, 1487, 1595

Offset: 1

Wesley Ivan Hurt, Jun 12 2024

Fill an array with the natural numbers n = 1,2,... along diagonals in alternating 'down' and 'up' directions. a(n) is row 2 of the boustrophedon-style array (see example).

In general, row k is given by (1+t^2+(n-k)*(-1)^t)/2, t = n+k-1. Here, k=2.

			       [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9] [10] [11] [12]
  [ 1]   1    3    4   10   11   21   22   36   37   55   56   78   ...
  [ 2]   2    5    9   12   20   23   35   38   54   57   77   ...
  [ 3]   6    8   13   19   24   34   39   53   58   76   ...
  [ 4]   7   14   18   25   33   40   52   59   75   ...
  [ 5]  15   17   26   32   41   51   60   74   ...
  [ 6]  16   27   31   42   50   61   73   ...
  [ 7]  28   30   43   49   62   72   ...
  [ 8]  29   44   48   63   71   ...
  [ 9]  45   47   64   70   ...
  [10]  46   65   69   ...
  [11]  66   68   ...
  [12]  67   ...
        ...

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

For rows k = 1..10: A131179 (k=1) n>0, this sequence (k=2), A373663 (k=3), A374004 (k=4), A374005 (k=5), A374007 (k=6), A374008 (k=7), A374009 (k=8), A374010 (k=9), A374011 (k=10).
Cf. A001844, A038722.
Row n=2 of A056011.
Column k=2 of A056023.

[(1 + (n+1)^2 - (n-2)*(-1)^n)/2: n in [1..80]];

k := 2; Table[(1 + (n+k-1)^2 + (n-k) (-1)^(n+k-1))/2, {n, 80}]

def A373662(n): return ((n+1)*(n+2)-1 if n&1 else n*(n+1)+5)>>1 # Chai Wah Wu, Jun 23 2024

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
a(n) = A131179(n+1) + (-1)^n.
G.f.: -x*(2*x^4-3*x^3+3*x+2)/((x+1)^2*(x-1)^3). - Alois P. Heinz, Jun 12 2024

A373663 a(n) = (1 + (n+2)^2 + (n-3)*(-1)^n)/2.

Original entry on oeis.org

6, 8, 13, 19, 24, 34, 39, 53, 58, 76, 81, 103, 108, 134, 139, 169, 174, 208, 213, 251, 256, 298, 303, 349, 354, 404, 409, 463, 468, 526, 531, 593, 598, 664, 669, 739, 744, 818, 823, 901, 906, 988, 993, 1079, 1084, 1174, 1179, 1273, 1278, 1376, 1381, 1483, 1488, 1594

Offset: 1

Wesley Ivan Hurt, Jun 12 2024

Fill an array with the natural numbers n = 1,2,... along diagonals in alternating 'down' and 'up' directions. a(n) is row 3 of the boustrophedon-style array (see example).

In general, row k is given by (1+t^2+(n-k)*(-1)^t)/2, t = n+k-1. Here, k=3.

			       [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9] [10] [11] [12]
  [ 1]   1    3    4   10   11   21   22   36   37   55   56   78   ...
  [ 2]   2    5    9   12   20   23   35   38   54   57   77   ...
  [ 3]   6    8   13   19   24   34   39   53   58   76   ...
  [ 4]   7   14   18   25   33   40   52   59   75   ...
  [ 5]  15   17   26   32   41   51   60   74   ...
  [ 6]  16   27   31   42   50   61   73   ...
  [ 7]  28   30   43   49   62   72   ...
  [ 8]  29   44   48   63   71   ...
  [ 9]  45   47   64   70   ...
  [10]  46   65   69   ...
  [11]  66   68   ...
  [12]  67   ...
        ...

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

For rows k = 1..10: A131179 (k=1) n>0, A373662 (k=2), this sequence (k=3), A374004 (k=4), A374005 (k=5), A374007 (k=6), A374008 (k=7), A374009 (k=8), A374010 (k=9), A374011 (k=10).

Row 3 of the example in A056011, Column 3 of the rectangular array in A056023.

[(1 + (n+2)^2 + (n-3)*(-1)^n)/2: n in [1..80]];

k := 3; Table[(1 + (n+k-1)^2 + (n-k) (-1)^(n+k-1))/2, {n, 80}]

def A373663(n): return ((n+1)*(n+2)+6 if n&1 else (n+2)*(n+3)-4)>>1 # Chai Wah Wu, Jun 23 2024

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
a(n) = A373662(n+1) - (-1)^n.
G.f.: -x*(x^4+2*x^3-7*x^2+2*x+6)/((x+1)^2*(x-1)^3).

A374004 a(n) = (1 + (n+3)^2 - (n-4)*(-1)^n)/2.

Original entry on oeis.org

7, 14, 18, 25, 33, 40, 52, 59, 75, 82, 102, 109, 133, 140, 168, 175, 207, 214, 250, 257, 297, 304, 348, 355, 403, 410, 462, 469, 525, 532, 592, 599, 663, 670, 738, 745, 817, 824, 900, 907, 987, 994, 1078, 1085, 1173, 1180, 1272, 1279, 1375, 1382, 1482, 1489, 1593

Offset: 1

Wesley Ivan Hurt, Jun 24 2024

Fill an array with the natural numbers n = 1,2,... along diagonals in alternating 'down' and 'up' directions. a(n) is row 4 of the boustrophedon-style array (see example).

In general, row k is given by (1+t^2+(n-k)*(-1)^t)/2, t = n+k-1. Here, k=4.

			       [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9] [10] [11] [12]
  [ 1]   1    3    4   10   11   21   22   36   37   55   56   78   ...
  [ 2]   2    5    9   12   20   23   35   38   54   57   77   ...
  [ 3]   6    8   13   19   24   34   39   53   58   76   ...
  [ 4]   7   14   18   25   33   40   52   59   75   ...
  [ 5]  15   17   26   32   41   51   60   74   ...
  [ 6]  16   27   31   42   50   61   73   ...
  [ 7]  28   30   43   49   62   72   ...
  [ 8]  29   44   48   63   71   ...
  [ 9]  45   47   64   70   ...
  [10]  46   65   69   ...
  [11]  66   68   ...
  [12]  67   ...
        ...

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

For rows k = 1..10: A131179 (k=1) n>0, A373662 (k=2), A373663 (k=3), this sequence (k=4), A374005 (k=5), A374007 (k=6), A374008 (k=7), A374009 (k=8), A374010 (k=9), A374011 (k=10).
Row 4 of the table in A056011.
Column 4 of the rectangular array in A056023.

[(1 + (n+3)^2 - (n-4)*(-1)^n)/2: n in [1..80]];

CoefficientList[Series[-(7*x^4 - 7*x^3 - 10*x^2 + 7 x + 7)/((x + 1)^2*(x - 1)^3), {x, 0, 50}], x]
k := 4; Table[(1 + (n+k-1)^2 + (n-k) (-1)^(n+k-1))/2, {n, 80}]

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
G.f.: -x*(7*x^4-7*x^3-10*x^2+7x+7)/((x+1)^2*(x-1)^3).
a(n) = A373663(n+1) + (-1)^n.

A374005 a(n) = (1 + (n+4)^2 + (n-5)*(-1)^n)/2.

Original entry on oeis.org

15, 17, 26, 32, 41, 51, 60, 74, 83, 101, 110, 132, 141, 167, 176, 206, 215, 249, 258, 296, 305, 347, 356, 402, 411, 461, 470, 524, 533, 591, 600, 662, 671, 737, 746, 816, 825, 899, 908, 986, 995, 1077, 1086, 1172, 1181, 1271, 1280, 1374, 1383, 1481, 1490, 1592, 1601

Offset: 1

Wesley Ivan Hurt, Jun 24 2024

Fill an array with the natural numbers n = 1,2,... along diagonals in alternating 'down' and 'up' directions. a(n) is row 5 of the boustrophedon-style array (see example).

In general, row k is given by (1+t^2+(n-k)*(-1)^t)/2, t = n+k-1. Here, k=5.

			       [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9] [10] [11] [12]
  [ 1]   1    3    4   10   11   21   22   36   37   55   56   78   ...
  [ 2]   2    5    9   12   20   23   35   38   54   57   77   ...
  [ 3]   6    8   13   19   24   34   39   53   58   76   ...
  [ 4]   7   14   18   25   33   40   52   59   75   ...
  [ 5]  15   17   26   32   41   51   60   74   ...
  [ 6]  16   27   31   42   50   61   73   ...
  [ 7]  28   30   43   49   62   72   ...
  [ 8]  29   44   48   63   71   ...
  [ 9]  45   47   64   70   ...
  [10]  46   65   69   ...
  [11]  66   68   ...
  [12]  67   ...
        ...

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

For rows k = 1..10: A131179 (k=1) n>0, A373662 (k=2), A373663 (k=3), A374004 (k=4), this sequence (k=5), A374007 (k=6), A374008 (k=7), A374009 (k=8), A374010 (k=9), A374011 (k=10).
Row 5 of the table in A056011.
Column 5 of the rectangular array in A056023.

[(1 + (n+4)^2 + (n-5)*(-1)^n)/2: n in [1..80]];

CoefficientList[Series[-(6*x^4 + 2*x^3 - 21*x^2 + 2*x + 15)/((x + 1)^2*(x - 1)^3), {x, 0, 50}], x]
k := 5; Table[(1 + (n + k - 1)^2 + (n - k) (-1)^(n + k - 1))/2, {n, 80}]

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
G.f.: -x*(6*x^4+2*x^3-21*x^2+2*x+15)/((x+1)^2*(x-1)^3).
a(n) = A374004(n+1) - (-1)^n.

A374007 a(n) = (1 + (n+5)^2 - (n-6)*(-1)^n)/2.

Original entry on oeis.org

16, 27, 31, 42, 50, 61, 73, 84, 100, 111, 131, 142, 166, 177, 205, 216, 248, 259, 295, 306, 346, 357, 401, 412, 460, 471, 523, 534, 590, 601, 661, 672, 736, 747, 815, 826, 898, 909, 985, 996, 1076, 1087, 1171, 1182, 1270, 1281, 1373, 1384, 1480, 1491, 1591, 1602

Offset: 1

Wesley Ivan Hurt, Jun 24 2024

Fill an array with the natural numbers n = 1,2,... along diagonals in alternating 'down' and 'up' directions. a(n) is row 6 of the boustrophedon-style array (see example).

In general, row k is given by (1+t^2+(n-k)*(-1)^t)/2, t = n+k-1. Here, k=6.

			       [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9] [10] [11] [12]
  [ 1]   1    3    4   10   11   21   22   36   37   55   56   78   ...
  [ 2]   2    5    9   12   20   23   35   38   54   57   77   ...
  [ 3]   6    8   13   19   24   34   39   53   58   76   ...
  [ 4]   7   14   18   25   33   40   52   59   75   ...
  [ 5]  15   17   26   32   41   51   60   74   ...
  [ 6]  16   27   31   42   50   61   73   ...
  [ 7]  28   30   43   49   62   72   ...
  [ 8]  29   44   48   63   71   ...
  [ 9]  45   47   64   70   ...
  [10]  46   65   69   ...
  [11]  66   68   ...
  [12]  67   ...
        ...

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

For rows k = 1..10: A131179 (k=1) n>0, A373662 (k=2), A373663 (k=3), A374004 (k=4), A374005 (k=5), this sequence (k=6), A374008 (k=7), A374009 (k=8), A374010 (k=9), A374011 (k=10).
Row 6 of the table in A056011.
Column 6 of the rectangular array in A056023.

[(1 + (n+5)^2 - (n-6)*(-1)^n)/2: n in [1..80]];

CoefficientList[Series[-(16*x^4 - 11*x^3 - 28*x^2 + 11*x + 16)/((x + 1)^2*(x - 1)^3), {x, 0, 50}], x]
k := 6; Table[(1 + (n + k - 1)^2 + (n - k) (-1)^(n + k - 1))/2, {n, 80}]

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
G.f.: -x*(16*x^4-11*x^3-28*x^2+11*x+16)/((x+1)^2*(x-1)^3).
a(n) = A374005(n+1) + (-1)^n.

A374008 a(n) = (1 + (n+6)^2 + (n-7)*(-1)^n)/2.

Original entry on oeis.org

28, 30, 43, 49, 62, 72, 85, 99, 112, 130, 143, 165, 178, 204, 217, 247, 260, 294, 307, 345, 358, 400, 413, 459, 472, 522, 535, 589, 602, 660, 673, 735, 748, 814, 827, 897, 910, 984, 997, 1075, 1088, 1170, 1183, 1269, 1282, 1372, 1385, 1479, 1492, 1590, 1603, 1705

Offset: 1

Wesley Ivan Hurt, Jun 24 2024

Fill an array with the natural numbers n = 1,2,... along diagonals in alternating 'down' and 'up' directions. a(n) is row 7 of the boustrophedon-style array (see example).

In general, row k is given by (1+t^2+(n-k)*(-1)^t)/2, t = n+k-1. Here, k=7.

			       [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9] [10] [11] [12]
  [ 1]   1    3    4   10   11   21   22   36   37   55   56   78   ...
  [ 2]   2    5    9   12   20   23   35   38   54   57   77   ...
  [ 3]   6    8   13   19   24   34   39   53   58   76   ...
  [ 4]   7   14   18   25   33   40   52   59   75   ...
  [ 5]  15   17   26   32   41   51   60   74   ...
  [ 6]  16   27   31   42   50   61   73   ...
  [ 7]  28   30   43   49   62   72   ...
  [ 8]  29   44   48   63   71   ...
  [ 9]  45   47   64   70   ...
  [10]  46   65   69   ...
  [11]  66   68   ...
  [12]  67   ...
        ...

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

For rows k = 1..10: A131179 (k=1) n>0, A373662 (k=2), A373663 (k=3), A374004 (k=4), A374005 (k=5), A374007 (k=6), this sequence (k=7), A374009 (k=8), A374010 (k=9), A374011 (k=10).
Row 7 of the table in A056011.
Column 7 of the rectangular array in A056023.

[(1 + (n+6)^2 + (n-7)*(-1)^n)/2: n in [1..80]];

CoefficientList[Series[-(15*x^4 + 2*x^3 - 43*x^2 + 2 x + 28)/((x + 1)^2*(x - 1)^3), {x, 0, 50}], x]
k := 7; Table[(1 + (n + k - 1)^2 + (n - k) (-1)^(n + k - 1))/2, {n, 80}]

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
G.f.: -x*(15*x^4+2*x^3-43*x^2+2x+28)/((x+1)^2*(x-1)^3).
a(n) = A374007(n+1) - (-1)^n.

A374009 a(n) = (1 + (n+7)^2 - (n-8)*(-1)^n)/2.

Original entry on oeis.org

29, 44, 48, 63, 71, 86, 98, 113, 129, 144, 164, 179, 203, 218, 246, 261, 293, 308, 344, 359, 399, 414, 458, 473, 521, 536, 588, 603, 659, 674, 734, 749, 813, 828, 896, 911, 983, 998, 1074, 1089, 1169, 1184, 1268, 1283, 1371, 1386, 1478, 1493, 1589, 1604, 1704, 1719

Offset: 1

Wesley Ivan Hurt, Jun 24 2024

Fill an array with the natural numbers n = 1,2,... along diagonals in alternating 'down' and 'up' directions. a(n) is row 8 of the boustrophedon-style array (see example).

In general, row k is given by (1+t^2+(n-k)*(-1)^t)/2, t = n+k-1. Here, k=8.

			       [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9] [10] [11] [12]
  [ 1]   1    3    4   10   11   21   22   36   37   55   56   78   ...
  [ 2]   2    5    9   12   20   23   35   38   54   57   77   ...
  [ 3]   6    8   13   19   24   34   39   53   58   76   ...
  [ 4]   7   14   18   25   33   40   52   59   75   ...
  [ 5]  15   17   26   32   41   51   60   74   ...
  [ 6]  16   27   31   42   50   61   73   ...
  [ 7]  28   30   43   49   62   72   ...
  [ 8]  29   44   48   63   71   ...
  [ 9]  45   47   64   70   ...
  [10]  46   65   69   ...
  [11]  66   68   ...
  [12]  67   ...
        ...

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

For rows k = 1..10: A131179 (k=1) n>0, A373662 (k=2), A373663 (k=3), A374004 (k=4), A374005 (k=5), A374007 (k=6), A374008 (k=7), this sequence (k=8), A374010 (k=9), A374011 (k=10).
Row 8 of the table in A056011.
Column 8 of the rectangular array in A056023.

[(1 + (n+7)^2 - (n-8)*(-1)^n)/2: n in [1..80]];

CoefficientList[Series[-(29*x^4 - 15*x^3 - 54*x^2 + 15*x + 29)/((x + 1)^2*(x - 1)^3), {x, 0, 50}], x]
k := 8; Table[(1 + (n + k - 1)^2 + (n - k) (-1)^(n + k - 1))/2, {n, 80}]

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
G.f.: -x*(29*x^4-15*x^3-54*x^2+15*x+29)/((x+1)^2*(x-1)^3).
a(n) = A374008(n+1) + (-1)^n.

A374011 a(n) = (1 + (n+9)^2 - (n-10)*(-1)^n)/2.

Original entry on oeis.org

46, 65, 69, 88, 96, 115, 127, 146, 162, 181, 201, 220, 244, 263, 291, 310, 342, 361, 397, 416, 456, 475, 519, 538, 586, 605, 657, 676, 732, 751, 811, 830, 894, 913, 981, 1000, 1072, 1091, 1167, 1186, 1266, 1285, 1369, 1388, 1476, 1495, 1587, 1606, 1702, 1721, 1821

Offset: 1

Wesley Ivan Hurt, Jun 24 2024

Fill an array with the natural numbers n = 1,2,... along diagonals in alternating 'down' and 'up' directions. a(n) is row 10 of the boustrophedon-style array (see example).

In general, row k is given by (1+t^2+(n-k)*(-1)^t)/2, t = n+k-1. Here, k=10.

			       [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9] [10] [11] [12]
  [ 1]   1    3    4   10   11   21   22   36   37   55   56   78   ...
  [ 2]   2    5    9   12   20   23   35   38   54   57   77   ...
  [ 3]   6    8   13   19   24   34   39   53   58   76   ...
  [ 4]   7   14   18   25   33   40   52   59   75   ...
  [ 5]  15   17   26   32   41   51   60   74   ...
  [ 6]  16   27   31   42   50   61   73   ...
  [ 7]  28   30   43   49   62   72   ...
  [ 8]  29   44   48   63   71   ...
  [ 9]  45   47   64   70   ...
  [10]  46   65   69   ...
  [11]  66   68   ...
  [12]  67   ...
        ...

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

For rows k = 1..10: A131179 (k=1) n>0, A373662 (k=2), A373663 (k=3), A374004 (k=4), A374005 (k=5), A374007 (k=6), A374008 (k=7), A374009 (k=8), A374010 (k=9), this sequence (k=10).
Row 10 of the table in A056011.
Column 10 of the rectangular array in A056023.

[(1 + (n+9)^2 - (n-10)*(-1)^n)/2: n in [1..80]];

CoefficientList[Series[-(46*x^4 - 19*x^3 - 88*x^2 + 19*x + 46)/((x + 1)^2*(x - 1)^3), {x, 0, 50}], x]
k := 10; Table[(1 + (n + k - 1)^2 + (n - k) (-1)^(n + k - 1))/2, {n, 80}]

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
G.f.: -x*(46*x^4-19*x^3-88*x^2+19*x+46)/((x+1)^2*(x-1)^3).
a(n) = A374010(n+1) + (-1)^n.

cp's OEIS Frontend

A131179 a(n) = if n mod 2 == 0 then n*(n+1)/2, otherwise (n-1)*n/2 + 1.

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A373662 a(n) = (1 + (n+1)^2 - (n-2)*(-1)^n)/2.

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A373663 a(n) = (1 + (n+2)^2 + (n-3)*(-1)^n)/2.

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A374004 a(n) = (1 + (n+3)^2 - (n-4)*(-1)^n)/2.

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A374005 a(n) = (1 + (n+4)^2 + (n-5)*(-1)^n)/2.

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A374007 a(n) = (1 + (n+5)^2 - (n-6)*(-1)^n)/2.

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A374008 a(n) = (1 + (n+6)^2 + (n-7)*(-1)^n)/2.

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A131179 a(n) = if n mod 2 == 0 then n(n+1)/2, otherwise (n-1)n/2 + 1.