cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A027672 Molien series for unitary 16-dimensional full Siegel modular group H_4 of order 48514675507200.

Original entry on oeis.org

1, 0, 1, 1, 2, 3, 7, 7, 19, 27, 52, 87, 172, 279, 550, 960, 1782, 3183, 5845, 10288, 18508, 32284, 56345, 96473, 164157, 274194, 454518, 741321, 1196924, 1906123, 3003750, 4673470, 7198311, 10959836, 16523847, 24654860, 36447873, 53369530, 77478005, 111498073
Offset: 0

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Author

N. J. A. Sloane

Keywords

Examples

			1+x^8+x^12+2*x^16+3*x^20+7*x^24+7*x^28+19*x^32+27*x^36+O(x^40).

Links

Crossrefs

Cf. A027633, A027638, A051354.

Programs

  • Mathematica
    (* See link for Mathematica program. *)

Formula

Oura gives an explicit formula for the Molien series.

A039946 Expansion of Molien series for 8-dimensional complex Clifford group of genus 3 and order 743178240.

Original entry on oeis.org

1, 1, 2, 5, 9, 16, 31, 53, 89, 152, 245, 384, 601, 911, 1351, 1986, 2856, 4037, 5653, 7791, 10592, 14268, 18990, 24999, 32643, 42218, 54112, 68869, 86971, 109014, 135812, 168101, 206769, 252990, 307849, 372616, 448934, 538348
Offset: 0

Views

Author

E. M. Rains

Keywords

Examples

			G.f. = 1 + x^8 + 2*x^16 + 5*x^24 + 9*x^32 + 16*x^40 + 31*x^48 + ...

Links

Crossrefs

Bisection of A027633. Cf. A008621, A008718, A024186, A008620, A028288, A043330, A051354.

Programs

  • Maple
    f(x):= (1 +x^3 +3*x^4 +3*x^5 +6*x^6 +8*x^7 +12*x^8 +18*x^9 +25*x^10 +29*x^11 +40*x^12 +50*x^13 +58*x^14 +69*x^15 +80*x^16 +85*x^17 +96*x^18 +104*x^19 +107*x^20 +109*x^21 +112*x^22 +109*x^23+107*x^24 +104*x^25 +96*x^26 +85*x^27 +80*x^28 +69*x^29 +58*x^30 +50*x^31 +40*x^32 +29*x^33 +25*x^34 +18*x^35 +12*x^36 +8*x^37 +6*x^38 +3*x^39 +3*x^40 +x^41 +x^44) / ( (1-x)^2*(1-x^3)^4*(1-x^5)^2*(1 +x +2*x^3 +2*x^4 + x^5 +4*x^6 +2*x^7 +x^8 +5*x^9 +2*x^10 +2*x^11 +5*x^12 +x^13 +2*x^14 + 4*x^15 +x^16 +2*x^17 +2*x^18 +x^20 +x^21) ); seq(coeff(series(f(x), x, n+1), x, n), n = 0..40);
  • Mathematica
    CoefficientList[Series[(1+x^3+3*x^4+3*x^5+6*x^6+8*x^7+12*x^8+18*x^9+25*x^10 + 29*x^11+40*x^12+50*x^13+58*x^14+69*x^15+80*x^16+85*x^17+96*x^18+104*x^19 + 107*x^20+109*x^21+112*x^22+109*x^23+107*x^24+104*x^25+96*x^26+85*x^27+80*x^28 +69*x^29+58*x^30+50*x^31+40*x^32+29*x^33+25*x^34+18*x^35+12*x^36 + 8*x^37 + 6*x^38+3*x^39+3*x^40+x^41+x^44)/((1-x)^2*(1-x^3)^4*(1-x^5)^2*(1+x+2*x^3+2*x^4 +x^5+4*x^6+2*x^7+x^8+5*x^9+2*x^10+2*x^11+5*x^12+x^13+2*x^14+4*x^15+x^16+2*x^17 +2*x^18+x^20+x^21)), {x,0,40}], x] (* G. C. Greubel, Feb 01 2020 *)
LinearRecurrence[{1,1,1,-2,-1,0,1,-1,1,0,0,-1,1,2,1,-3,-2,0,2,1,-1,0,0,-1,1,2,0,-2,-3,1,2,1,-1,0,0,1,-1,1,0,-1,-2,1,1,1,-1},{1,1,2,5,9,16,31,53,89,152,245,384,601,911,1351,1986,2856,4037,5653,7791,10592,14268,18990,24999,32643,42218,54112,68869,86971,109014,135812,168101,206769,252990,307849,372616,448934,538348,642630,764021,904658,1066943,1253876,1468340,1713529},40] (* Harvey P. Dale, Jul 04 2021 *)

Formula

G.f.: (1 +x^24 +3*x^32 +3*x^40 +6*x^48 +8*x^56 +12*x^64 +18*x^72 +25*x^80 +29*x^88 +40*x^96 +50*x^104 +58*x^112 +69*x^120 +80*x^128 +85*x^136 +96*x^144 +104*x^152 +107*x^160 +109*x^168 +112*x^176 +109*x^184 +107*x^192 +104*x^200 +96*x^208 +85*x^216 +80*x^224 +69*x^232 +58*x^240 +50*x^248 +40*x^256 +29*x^264 +25*x^272 +18*x^280 +12*x^288 +8*x^296 +6*x^304 +3*x^312 +3*x^320 +x^328 +x^352) / ( (1-x^8)^2*(1-x^24)^4*(1-x^40)^2*(1 +x^8 +2*x^24 +2*x^32 + x^40 +4*x^48 +2*x^56 +x^64 +5*x^72 +2*x^80 +2*x^88 +5*x^96 +x^104 +2*x^112 + 4*x^120 +x^128 +2*x^136 +2*x^144 +x^160 +x^168) ), nonzero terms.
G.f.: (1 +x^3 +3*x^4 +3*x^5 +6*x^6 +8*x^7 +12*x^8 +18*x^9 +25*x^10 +29*x^11 +40*x^12 +50*x^13 +58*x^14 +69*x^15 +80*x^16 +85*x^17 +96*x^18 +104*x^19 +107*x^20 +109*x^21 +112*x^22 +109*x^23+107*x^24 +104*x^25 +96*x^26 +85*x^27 +80*x^28 +69*x^29 +58*x^30 +50*x^31 +40*x^32 +29*x^33 +25*x^34 +18*x^35 +12*x^36 +8*x^37 +6*x^38 +3*x^39 +3*x^40 +x^41 +x^44) / ( (1-x)^2*(1-x^3)^4*(1-x^5)^2*(1 +x +2*x^3 +2*x^4 + x^5 +4*x^6 +2*x^7 +x^8 +5*x^9 +2*x^10 +2*x^11 +5*x^12 +x^13 +2*x^14 + 4*x^15 +x^16 +2*x^17 +2*x^18 +x^20 +x^21) ). - G. C. Greubel, Feb 01 2020

Extensions

Typo in reduced g.f.s. corrected by Georg Fischer, Apr 18 2020

A144060 Expansion of Molien series for the ring of genus 5 code polynomials for Type II codes.

Original entry on oeis.org

1, 0, 1, 0, 2, 2, 8, 8, 34, 60, 203, 553, 2063, 7359, 30811, 127416, 541644, 2235677, 8966371, 34413747, 126465849, 443858877, 1490702752, 4796609651, 14821521743, 44071296447, 126388352322, 350298687803, 940211047828, 2448320130626, 6196158876181
Offset: 0

Views

Author

N. J. A. Sloane, Dec 22 2008, following a suggestion from G. Nebe

Keywords

Examples

			1 + x^8 + 2*x^16 + 2*x^20 + 8*x^24 + 8*x^28 + 34*x^32 + 60*x^36 + 203*x^40 + 553*x^44 + 2063*x^48 + 7359*x^52 + 30811*x^56 + 127416*x^60 + 541644*x^64 + 2235677*x^68 + 8966371*x^72 + 34413747*x^76 + 126465849*x^80 + 443858877*x^84 + 1490702752*x^88 + 4796609651*x^92 + 14821521743*x^96 + .....

Links

Crossrefs

Cf. A027672, A051354.

Programs

  • Mathematica
    (* See link for Mathematica program. *)

Formula

Oura (see link) gives the Molien series explicitly.

Extensions

More terms from Ray Chandler, Mar 23 2017
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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