A000432
Series-parallel numbers.
Original entry on oeis.org
8, 52, 288, 1424, 6648, 29700, 128800, 545600, 2269672, 9303140, 37672216, 150998016, 599988696, 2366216164, 9270987656, 36116062832, 139978757920, 540069059028, 2075217121688, 7944690769952, 30313624200640, 115312027433188, 437420730644304, 1655047867097280, 6247339311097296, 23530440547115428, 88447214709073696, 331832490378209152, 1242766581420901656, 4646714574562484628, 17347357264162110368, 64668460220964604944, 240747014238189337840, 895102104022837748484, 3323982608759454833032, 12329573838525875316560, 45684294664598118867184, 169098457957523787786644
Offset: 3
- J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 142.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
-
n = 38; s = 1/(1 - x) + O[x]^(n + 1); Do[s = s/(1 - x^k)^Coefficient[s, x^k] + O[x]^(n + 1), {k, 2, n}] ; S = s - 1; CoefficientList[4 (2 + S) (1 + S)/(1 - S)^5 + O[x]^n, x] (* Jean-François Alcover, Feb 09 2016 *)
A000527
Series-parallel numbers.
Original entry on oeis.org
52, 472, 3224, 18888, 101340, 511120, 2465904, 11496144, 52165892, 231557064, 1009247192, 4331502840, 18346242492, 76822836544, 318485778848, 1308750158016, 5335993098340, 21603437175288, 86912657626392, 347660876627944, 1383457374046444, 5479086968052912, 21604984733546336, 84850331177724944, 332001521469767940, 1294589169323791912, 5031934808360234760, 19500424806065865400, 75360646947991208396, 290478417300879735680, 1116919455364101145920, 4284817000807140094464, 16402243457215852326116, 62659647762404302956856, 238910441445219175239480
Offset: 4
- J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 142.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
-
n = 35; s = 1/(1 - x) + O[x]^(n + 1); Do[s = s/(1 - x^k)^Coefficient[s, x^k] + O[x]^(n + 1), {k, 2, n}] ; S = s - 1; CoefficientList[4 (13 + 14 S + 3 S^2) (1 + S)/(1 - S)^7 + O[x]^n, x] (* Jean-François Alcover, Feb 09 2016 *)
A232005
Number of distinct resistances that can be produced from a circuit of resistors with resistances 1, 2, ..., n using only series and parallel combinations.
Original entry on oeis.org
1, 2, 8, 48, 386, 3781, 49475, 762869, 13554897, 266817541
Offset: 1
a(2) = 2 since given a 1-ohm and a 2-ohm resistor, a series circuit yields 3 ohms, while a parallel circuit yields 2/3 ohms, which thus yields two distinct resistances.
A292126
Number of two-terminal exclusive-bridged graphs with n edges.
Original entry on oeis.org
0, 0, 0, 0, 1, 4, 21, 86, 349, 1328, 4925, 17786
Offset: 1
Comments