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.

User: R. J. Mathar

R. J. Mathar's wiki page.

R. J. Mathar has authored 1471 sequences. Here are the ten most recent ones:

A387489 Number of packing 1X1X2 bricks into 2X2Xn boxes considering packings obtained by rigid motions equivalent.

Original entry on oeis.org

1, 1, 2, 7, 26, 71, 258, 857, 3148, 11300, 41841, 154140, 573201, 2129726, 7935779, 29569762, 110281431, 411333271, 1534676318, 5726191937, 21367848168, 79738762725, 297573920356, 1110521036955, 4144432037026, 15467004104026, 57723125759179, 215424338586742, 803971544759711, 3000455162798396, 11197833423648453, 41790839930063492, 155965434740272813, 582070675232252525
Offset: 0

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Author

R. J. Mathar, Aug 31 2025

Keywords

Comments

There seem to be several typos in Jepsen's equations. The enumeration here is derived from the expression of p(n) as 1/8ths of Psi(e)+2*Psi(rho)+Psi(rho^2)+2*Psi(sigma)+2*Psi(rho*sigma) if n>=3.

Links

Crossrefs

Cf. A109437 (is Jepsen's b(n)/4), A006253 (rigid motion symmetry ignored, Jepsen's a(n)).

Formula

G.f.: 1 +x +2*x^2 -x^3*(-7 +16*x +57*x^2 -118*x^3 -38*x^4 +30*x^5 -53*x^6 +127*x^7 +42*x^8 -49*x^9 -7*x^10 +4*x^11) / ( (x-1)*(1+x) *(x^2+2*x-1) *(x^2+1) *(x^2-4*x+1) *(x^4-4*x^2+1) ).

A387454 Decimal expansion of cos(Pi/21).

Original entry on oeis.org

9, 8, 8, 8, 3, 0, 8, 2, 6, 2, 2, 5, 1, 2, 8, 5, 4, 5, 0, 6, 9, 7, 4, 2, 8, 8, 2, 9, 3, 4, 0, 0, 8, 6, 1, 3, 0, 6, 5, 2, 5, 1, 0, 1, 3, 5, 7, 4, 1, 8, 7, 7, 0, 6, 3, 9, 9, 4, 9, 6, 9, 2, 7, 1, 6, 0, 2, 1, 3, 5, 3, 3, 0, 9, 8, 7, 2, 6, 0, 9, 9, 2, 4, 9, 3, 4, 3, 1, 8, 9, 9, 6, 8, 1, 7, 4, 1, 9, 3, 0, 8, 6, 8, 8, 8, 7, 1, 7, 9, 1, 2, 9, 1, 6, 1, 0, 5, 1
Offset: 0

Views

Author

R. J. Mathar, Aug 29 2025

Keywords

Examples

			0.98883082622512854507...

Links

Crossrefs

Cf. A019688.

Formula

Equals sin(19/42*Pi).
Largest of the 6 real-valued roots of 64*x^6+32*x^5-96*x^4-48*x^3+32*x^2+16*x+1=0.
4*this^3 -3*this = A073052.
Equals 2F1(-1/14,1/14;1/2;3/4). - R. J. Mathar, Aug 31 2025

A387453 Decimal expansion of cos(Pi/29).

Original entry on oeis.org

9, 9, 4, 1, 3, 7, 9, 5, 7, 1, 5, 4, 3, 5, 9, 6, 0, 8, 9, 5, 5, 3, 0, 2, 7, 1, 5, 8, 7, 9, 5, 5, 1, 5, 6, 6, 8, 5, 4, 5, 5, 9, 6, 1, 8, 4, 8, 1, 3, 9, 3, 9, 3, 8, 2, 6, 4, 5, 2, 0, 3, 0, 2, 8, 4, 2, 0, 2, 8, 8, 1, 1, 5, 2, 3, 4, 4, 1, 8, 8, 8, 4, 3, 8, 5, 4, 2, 5, 5, 3, 5, 9, 7, 6, 8, 6, 7, 9, 3, 9, 2, 4, 0, 0, 6, 2, 4, 3, 2, 0, 9, 3, 6, 8, 8, 0, 4, 3
Offset: 0

Views

Author

R. J. Mathar, Aug 29 2025

Keywords

Examples

			0.99413795715435960896...

Links

Formula

Equals sin(27*Pi/58).
Largest of the 14 real-valued roots of 16384*x^14 -8192*x^13 -53248*x^12 +24576*x^11 +67584*x^10 -28160*x^9 -42240*x^8 +15360*x^7 +13440*x^6 -4032*x^5 -2016*x^4 +448*x^3 +112*x^2 -14*x -1 =0.

A387445 Decimal expansion of cos(Pi/25).

Original entry on oeis.org

9, 9, 2, 1, 1, 4, 7, 0, 1, 3, 1, 4, 4, 7, 7, 8, 3, 1, 0, 4, 9, 7, 9, 3, 0, 4, 2, 7, 8, 5, 7, 7, 8, 5, 2, 1, 4, 5, 3, 0, 3, 6, 7, 0, 8, 9, 6, 8, 7, 9, 5, 7, 3, 5, 8, 7, 1, 0, 2, 1, 2, 2, 6, 4, 1, 0, 8, 8, 3, 1, 1, 2, 2, 5, 2, 7, 1, 5, 3, 4, 1, 6, 1, 5, 3, 6, 7, 6, 6, 7, 7, 5, 3, 4, 5, 3, 9, 8, 5, 6, 4, 6, 2, 2, 3, 1, 6, 5, 0, 4, 8, 2, 8, 7, 2, 8, 1, 6
Offset: 0

Views

Author

R. J. Mathar, Aug 29 2025

Keywords

Examples

			0.99211470131447783105...

Links

Crossrefs

Cf. A019694.

Formula

Equals sin(23*Pi/50).
Largest of the 10 real-valued roots of 1024*x^10 -2560*x^8 +2240*x^6 -32*x^5 -800*x^4 +40*x^3 +100*x^2 -10*x -1 =0.
16*this^5 -20*this^3 +5*this = A019863.

A387442 Decimal expansion of cos(Pi/19).

Original entry on oeis.org

9, 8, 6, 3, 6, 1, 3, 0, 3, 4, 0, 2, 7, 2, 2, 3, 7, 3, 6, 0, 2, 5, 0, 9, 1, 9, 4, 8, 1, 9, 0, 6, 7, 1, 1, 0, 7, 2, 8, 4, 8, 1, 5, 0, 3, 2, 0, 2, 8, 7, 6, 3, 1, 6, 7, 4, 3, 6, 6, 5, 1, 3, 5, 0, 6, 3, 4, 5, 4, 0, 6, 6, 4, 9, 4, 3, 1, 9, 6, 0, 1, 6, 2, 8, 4, 7, 7, 9, 9, 7, 0, 7, 4, 1, 4, 5, 5, 0, 8, 1, 2, 9, 7, 0, 4, 1, 7, 2, 9, 7, 4, 9, 8, 1, 7, 2, 4, 5
Offset: 0

Views

Author

R. J. Mathar, Aug 29 2025

Keywords

Examples

			0.98636130340272237360...

Links

Crossrefs

Cf. A019686.

Formula

Equals sin(17*Pi/38).
Largest root of 512*x^9 -256*x^8 -1024*x^7 +448*x^6 +672*x^5 -240*x^4 -160*x^3 +40*x^2 +10*x -1 =0.

A387446 Decimal expansion of cos(Pi/26).

Original entry on oeis.org

9, 9, 2, 7, 0, 8, 8, 7, 4, 0, 9, 8, 0, 5, 3, 9, 9, 2, 8, 0, 0, 7, 5, 1, 6, 4, 9, 4, 9, 2, 5, 2, 0, 1, 7, 9, 3, 4, 3, 6, 7, 5, 6, 3, 2, 9, 7, 0, 1, 6, 6, 8, 5, 5, 7, 7, 0, 9, 9, 7, 5, 6, 0, 5, 1, 1, 8, 6, 7, 4, 4, 6, 2, 1, 3, 9, 6, 2, 9, 1, 4, 5, 5, 8, 6, 1, 6, 9, 4, 9, 3, 4, 2, 7, 8, 2, 4, 0, 4, 4, 1, 8, 9, 9, 1, 1, 8, 6, 0, 7, 1, 4, 1, 7, 7, 0, 9, 1
Offset: 0

Views

Author

R. J. Mathar, Aug 29 2025

Keywords

Examples

			0.99270887409805399280...

Links

Formula

Equals sin(6*Pi/13) = sqrt( (A387441+1)/2 ).
Largest of the 12 real-valued roots of 4096*x^12 -13312*x^10 +16640*x^8 -9984*x^6 +2912*x^4 -364*x^2 +13 = 0.

A387444 Decimal expansion of cos(Pi/23).

Original entry on oeis.org

9, 9, 0, 6, 8, 5, 9, 4, 6, 0, 3, 6, 3, 3, 0, 7, 5, 2, 3, 4, 2, 3, 2, 2, 9, 6, 0, 0, 9, 6, 2, 0, 6, 0, 0, 5, 1, 3, 9, 9, 9, 9, 1, 8, 3, 4, 5, 4, 8, 2, 4, 3, 9, 0, 6, 6, 0, 6, 5, 1, 3, 0, 4, 1, 9, 9, 7, 9, 6, 6, 4, 4, 9, 1, 2, 0, 1, 4, 8, 0, 5, 7, 9, 6, 9, 2, 2, 6, 0, 4, 2, 7, 1, 9, 2, 6, 9, 6, 9, 2, 9, 7, 4, 0, 1, 4, 5, 3, 7, 9, 9, 1, 4, 5, 5, 2, 5, 4
Offset: 0

Views

Author

R. J. Mathar, Aug 29 2025

Keywords

Examples

			0.99068594603633075234...

Links

Crossrefs

Cf. A019690.

Formula

Equals sin(21*Pi/46).
Largest of the 11 real-valued roots of 2048*x^11 -1024*x^10 -5120*x^9 +2304*x^8 +4608*x^7 -1792*x^6 -1792*x^5 +560*x^4 +280*x^3 -60*x^2 -12*x +1 = 0.

A387443 Decimal expansion of cos(Pi/22).

Original entry on oeis.org

9, 8, 9, 8, 2, 1, 4, 4, 1, 8, 8, 0, 9, 3, 2, 7, 3, 2, 3, 7, 6, 0, 9, 2, 0, 3, 7, 7, 7, 6, 7, 1, 8, 7, 8, 7, 3, 7, 6, 5, 1, 9, 3, 7, 1, 9, 4, 8, 7, 1, 6, 6, 8, 7, 8, 3, 8, 6, 1, 5, 4, 4, 4, 9, 2, 3, 6, 2, 2, 3, 6, 5, 7, 2, 5, 3, 5, 4, 0, 9, 8, 6, 0, 4, 4, 4, 2, 3, 3, 9, 8, 3, 8, 3, 5, 6, 6, 0, 3, 5, 9, 6, 8, 3, 7, 7, 5, 0, 2, 5, 8, 5, 6, 8, 1, 4, 2, 1
Offset: 0

Views

Author

R. J. Mathar, Aug 29 2025

Keywords

Examples

			0.98982144188093273238...

Links

Crossrefs

Cf. A019689.

Formula

Equals sin(5*Pi/11) = sqrt( (A387440+1)/2 ).
Largest of the 10 real-valued roots of 1024*x^10 -2816*x^8 +2816*x^6 -1232*x^4 +220*x^2 -11 =0.

A387447 Decimal expansion of cos(Pi/27).

Original entry on oeis.org

9, 9, 3, 2, 3, 8, 3, 5, 7, 7, 4, 1, 9, 4, 2, 9, 8, 8, 5, 4, 7, 8, 9, 5, 5, 5, 2, 1, 9, 3, 7, 0, 4, 3, 4, 0, 3, 4, 9, 1, 0, 6, 1, 9, 7, 0, 7, 0, 6, 9, 3, 7, 0, 2, 5, 6, 5, 0, 0, 7, 1, 8, 8, 0, 1, 6, 2, 7, 8, 6, 0, 5, 1, 5, 0, 5, 1, 2, 6, 3, 3, 6, 8, 0, 1, 7, 2, 0, 7, 1, 5, 3, 9, 2, 5, 9, 1, 2, 2, 5, 4, 3, 6, 1, 2, 1, 7, 2, 7, 0, 3, 5, 7, 6, 6, 3, 1, 6
Offset: 0

Views

Author

R. J. Mathar, Aug 29 2025

Keywords

Examples

			0.99323835774194298855...

Links

Formula

Equals sin(25*Pi/54) = 2F1(-1/18,1/18;1/2;3/4).
Largest of the 9 real-valued roots of 512*x^9 -1152*x^7 +864*x^5 -240*x^3 +18*x -1 =0.
4*this^3 -3*this = A019879.

A387448 Decimal expansion of cos(Pi/28).

Original entry on oeis.org

9, 9, 3, 7, 1, 2, 2, 0, 9, 8, 9, 3, 2, 4, 2, 5, 8, 3, 5, 3, 3, 1, 4, 8, 2, 4, 1, 9, 4, 7, 3, 7, 8, 6, 9, 7, 1, 5, 2, 6, 3, 5, 4, 9, 5, 7, 8, 2, 0, 7, 3, 2, 1, 4, 9, 2, 7, 7, 5, 6, 5, 0, 2, 1, 5, 9, 5, 1, 0, 3, 8, 0, 9, 6, 8, 8, 9, 0, 9, 4, 4, 6, 6, 9, 0, 9, 9, 5, 7, 6, 4, 8, 7, 2, 7, 0, 6, 4, 3, 8, 2, 2, 3, 5, 4, 3, 0, 0, 9, 0, 4, 5, 5, 3, 7, 6, 6, 8
Offset: 0

Views

Author

R. J. Mathar, Aug 29 2025

Keywords

Examples

			0.99371220989324258353...

Links

Crossrefs

Cf. A132744.

Formula

Equals sin(13*Pi/28) = sqrt( (A232735+1)/2 ) = 2F1(-1/14,1/14;1/2;1/2).
Largest of the 12 real-valued roots of 4096*x^12 -12288*x^10 +13568*x^8 -6656*x^6 +1376*x^4 -96*x^2 +1 =0.

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