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 1-10 of 13 results. Next

A027157 Triangular array T given T(n,k)=(1/2)*t(n+1,k+1), 0<=k<=n, n >= 0, t given by A027144.

Original entry on oeis.org

1, 2, 1, 3, 3, 4, 4, 6, 8, 4, 5, 10, 24, 12, 16, 6, 15, 40, 36, 32, 16, 7, 21, 76, 76, 144, 48, 64, 8, 28, 112, 152, 256, 192, 128, 64, 9, 36, 176, 264, 672, 448, 768, 192, 256, 10, 45, 240, 440, 1088, 1120, 1408, 960, 512, 256, 11, 55, 340, 680
Offset: 1

Views

Author

Clark Kimberling

Keywords

A027151 a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A027144.

Original entry on oeis.org

1, 3, 7, 21, 45, 135, 291, 873, 1881, 5643, 12159, 36477, 78597, 235791, 508059, 1524177, 3284145, 9852435, 21229047, 63687141, 137226717, 411680151, 887047443, 2661142329, 5733964809, 17201894427, 37064931183, 111194793549, 239591481525, 718774444575
Offset: 0

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A141041 (bisection), A287811 (bisection).

Programs

  • PARI
    Vec((1 + 3*x)*(1 + x^2) / (1 - 6*x^2 - 3*x^4) + O(x^40)) \\ Colin Barker, Jan 18 2018

Formula

G.f.: (1 + 3*x)*(1 + x^2) / (1 - 6*x^2 - 3*x^4).
a(n) = 6*a(n-2) + 3*a(n-4) for n>3. - Colin Barker, Jan 18 2018

A027145 a(n) = A027144(2n, n).

Original entry on oeis.org

1, 4, 12, 80, 304, 2176, 8832, 64768, 271104, 2013184, 8579072, 64200704, 276815872, 2082406400, 9053405184, 68364861440, 299056168960, 2264753766400, 9954207989760, 75553161871360, 333336432082944, 2534637351993344, 11217239353065472, 85421341058007040, 379009013460762624
Offset: 0

Views

Author

Clark Kimberling

Keywords

Extensions

More terms from Sean A. Irvine, Oct 24 2019

A027146 a(n) = A027144(2n, n-1).

Original entry on oeis.org

1, 8, 30, 224, 880, 6656, 27104, 206336, 859392, 6565888, 27765760, 212615168, 908943360, 6970998784, 30045757440, 230691307520, 1000634122240, 7689454223360, 33522958204928, 257783270211584, 1128501249835008, 8682602001072128, 38141362595430400, 293587672402755584
Offset: 1

Views

Author

Clark Kimberling

Keywords

Extensions

More terms from Sean A. Irvine, Oct 24 2019

A027147 a(n) = A027144(2n, n-2).

Original entry on oeis.org

1, 12, 56, 480, 2040, 16576, 69888, 557568, 2361600, 18675712, 79613952, 626409472, 2686867456, 21071708160, 90875494400, 711081984000, 3081088991232, 24069137760256, 104712901754880, 816979824869376, 3566715303624704, 27800440481513472, 121738713372819456, 948129286114508800
Offset: 2

Views

Author

Clark Kimberling

Keywords

Extensions

More terms from Sean A. Irvine, Oct 24 2019

A027148 a(n) = A027144(2n-1, n-1).

Original entry on oeis.org

1, 6, 20, 152, 528, 4416, 15488, 135552, 477440, 4289536, 15144960, 138407936, 489431040, 4526702592, 16024403968, 149528084480, 529747476480, 4977103994880, 17643662213120, 166668216041472, 591119702294528, 5608619676532736
Offset: 1

Views

Author

Clark Kimberling

Keywords

A027149 a(n) = A027144(2n-1, n-2).

Original entry on oeis.org

1, 10, 42, 352, 1360, 11616, 43680, 381952, 1416960, 12620800, 46441472, 419512320, 1535352832, 14021353472, 51117465600, 470886645760, 1711716106240, 15879295991808, 57592095965184, 537381547540480, 1945481074704384
Offset: 2

Views

Author

Clark Kimberling

Keywords

A027150 a(n) = A027144(n, floor(n/2)).

Original entry on oeis.org

1, 1, 4, 6, 12, 20, 80, 152, 304, 528, 2176, 4416, 8832, 15488, 64768, 135552, 271104, 477440, 2013184, 4289536, 8579072, 15144960, 64200704, 138407936, 276815872, 489431040, 2082406400, 4526702592, 9053405184, 16024403968
Offset: 0

Views

Author

Clark Kimberling

Keywords

A027152 T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A027144.

Original entry on oeis.org

1, 1, 5, 7, 21, 31, 123, 209, 601, 971, 3647, 6589, 18565, 31375, 114203, 213073, 593073, 1030675, 3674615, 6997477, 19315165, 34221463, 120206611, 232218425, 637066249, 1144951835, 3976689519, 7765255757, 21202165941, 38528688671
Offset: 0

Views

Author

Clark Kimberling

Keywords

A027153 a(n) = Sum_{0<=j<=i<=n} A027144(i, j).

Original entry on oeis.org

1, 4, 11, 32, 77, 212, 503, 1376, 3257, 8900, 21059, 57536, 136133, 371924, 879983, 2404160, 5688305, 15540740, 36769787, 100456928, 237683645, 649363796, 1536411239, 4197553568, 9931518377, 27133412804, 64198343987
Offset: 0

Views

Author

Clark Kimberling

Keywords

Crossrefs

Partial sums of A027151.
Showing 1-10 of 13 results. Next

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

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