A203163
(n-1)-st elementary symmetric function of the first n terms of (1,2,3,4,1,2,3,4,1,2,3,4,...) = A010883.
Original entry on oeis.org
1, 3, 11, 50, 74, 172, 564, 2400, 2976, 6528, 20736, 86400, 100224, 214272, 670464, 2764800, 3096576, 6524928, 20238336, 82944000, 90906624, 189775872, 585252864, 2388787200, 2579890176, 5350883328, 16434855936, 66886041600
Offset: 1
Let esf abbreviate "elementary symmetric function". Then
0th esf of {1}: 1;
1st esf of {1,2}: 1+2 = 3;
2nd esf of {1,2,3} is 1*2 + 1*3 + 2*3 = 11.
-
f[k_] := 1 + Mod[k + 3, 4]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 33}] (* A203163 *)
LinearRecurrence[{0,0,0,48,0,0,0,-576},{1,3,11,50,74,172,564,2400},50] (* Harvey P. Dale, Aug 18 2020 *)
-
Vec(x*(36*x^6+28*x^5+26*x^4+50*x^3+11*x^2+3*x+1)/(24*x^4-1)^2 + O(x^100)) \\ Colin Barker, Aug 15 2014
A203160
(n-1)-st elementary symmetric function of the first n terms of (2,3,1,2,3,1,2,3,1,...)=A010882.
Original entry on oeis.org
1, 5, 11, 28, 96, 132, 300, 972, 1188, 2592, 8208, 9504, 20304, 63504, 71280, 150336, 466560, 513216, 1073088, 3312576, 3592512, 7464960, 22954752, 24634368, 50948352, 156204288, 166281984, 342641664, 1048080384, 1108546560, 2277559296
Offset: 1
Let esf abbreviate "elementary symmetric function". Then
0th esf of {2}: 1,
1st esf of {2,3}: 2+3=5,
2nd esf of {2,3,1} is 2*3+2*1+3*1=11.
-
f[k_] := 1 + Mod[k, 3]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 33}] (* A203160 *)
LinearRecurrence[{0,0,12,0,0,-36},{1,5,11,28,96,132},40] (* Harvey P. Dale, Mar 19 2016 *)
-
Vec(x*(36*x^4+16*x^3+11*x^2+5*x+1)/(6*x^3-1)^2 + O(x^100)) \\ Colin Barker, Aug 15 2014
A203164
(n-1)-st elementary symmetric function of the first n terms of the periodic sequence (4,1,2,3,4,1,2,3,...).
Original entry on oeis.org
1, 5, 14, 50, 224, 320, 736, 2400, 10176, 12480, 27264, 86400, 359424, 414720, 884736, 2764800, 11390976, 12718080, 26763264, 82944000, 339738624, 371589120, 775028736, 2388787200, 9746251776, 10510663680, 21785739264, 66886041600
Offset: 1
-
f[k_] := 1 + Mod[k + 2, 4];
t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 33}] (* A203164 *)
A203165
(n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,4,1,2,3,4,1,2,...).
Original entry on oeis.org
1, 7, 19, 50, 174, 768, 1056, 2400, 7776, 32832, 39744, 86400, 273024, 1133568, 1299456, 2764800, 8626176, 35500032, 39481344, 82944000, 256794624, 1051066368, 1146617856, 2388787200, 7357464576, 30003167232, 32296402944, 66886041600
Offset: 1
-
f[k_] := 1 + Mod[k + 1, 4];
t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 33}] (* A203165 *)
A203161
(n-1)-st elementary symmetric function of the first n terms of (3,1,2,3,1,2,3,1,2,...).
Original entry on oeis.org
1, 4, 11, 39, 57, 132, 432, 540, 1188, 3780, 4428, 9504, 29808, 33696, 71280, 221616, 244944, 513216, 1586304, 1726272, 3592512, 11057472, 11897280, 24634368, 75582720, 80621568, 166281984, 508923648, 539156736, 1108546560, 3386105856
Offset: 1
Let esf abbreviate "elementary symmetric function". Then
0th esf of {3}: 1,
1st esf of {3,1}: 3+1=4,
2nd esf of {3,1,2} is 3*1+3*1+1*2=11.
-
f[k_] := 1 + Mod[k + 1, 3]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 33}] (* A203161 *)
-
Vec(x*(3*x+1)*(3*x^3+8*x^2+x+1)/(6*x^3-1)^2 + O(x^100)) \\ Colin Barker, Aug 15 2014
Showing 1-5 of 5 results.
Comments