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 10 results.

A047141 Sum{T(i,n-i): i=0,1,...,n}, array T as in A047140.

Original entry on oeis.org

1, 2, 4, 6, 12, 20, 40, 80, 160, 320, 578, 1156, 2132, 4264, 8528, 17056, 34112, 64384, 128768, 245292, 490584, 981168, 1962336, 3924672, 7556046, 15112092, 29246744, 58493488, 116986976, 233973952, 467947904, 911000006, 1822000012
Offset: 0

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A047142 T(n,n), array T as in A047140.

Original entry on oeis.org

1, 2, 4, 10, 38, 142, 470, 1576, 5940, 22714, 83456, 305088, 1158606, 4456076, 16946498, 64189932, 246350606, 952607962, 3675557676, 14158562010, 54805236890, 213011072542, 828185178452, 3219077811678, 12537974366478
Offset: 0

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A047143 T(n,n-1), array T as in A047140.

Original entry on oeis.org

1, 3, 8, 23, 80, 290, 1010, 3521, 12934, 48498, 180020, 666648, 2512214, 9569120, 36408682, 138417669, 529685612, 2038304708, 7852427512, 30259337658, 116937868076, 453269554872, 1759337897040, 6833437297968, 26582114114294
Offset: 1

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A047144 T(n,n-2), array T as in A047140.

Original entry on oeis.org

1, 4, 13, 42, 148, 540, 1945, 6994, 25784, 96564, 361560, 1353608, 5113044, 19462184, 74227737, 283335006, 1085696746, 4176869836, 16100775648, 62132631186, 240258482330, 931152718588, 3614359486290, 14044139747816
Offset: 2

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A047145 T(n,n-3), array T as in A047140.

Original entry on oeis.org

1, 5, 19, 68, 250, 935, 3473, 12850, 48066, 181540, 686960, 2600830, 9893064, 37819055, 144917337, 556011134, 2138565128, 8248348136, 31873293528, 123320614254, 477883163716, 1855021589250, 7210702449848, 28058894828756
Offset: 3

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A047146 T(n,n+1), array T as in A047140.

Original entry on oeis.org

1, 1, 2, 15, 62, 180, 566, 2419, 9780, 34958, 125068, 491958, 1943862, 7377378, 27781250, 107932937, 422922350, 1637252968, 6306134498, 24545899232, 96073204466, 374915623580, 1459739914638, 5704537068510, 22360905044350
Offset: 0

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Crossrefs

Cf. A047140.

A047147 T(n,n+2), array T as in A047140.

Original entry on oeis.org

1, 2, 5, 24, 38, 96, 843, 3840, 12244, 41612, 186870, 785256, 2921302, 10834752, 43743005, 176571744, 684645006, 2630576822, 10387337222, 41267967576, 161904551038, 631554736186, 2485459256832, 9822930677872, 38685615768302
Offset: 0

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A047148 T(n,n+3), array T as in A047140.

Original entry on oeis.org

1, 3, 9, 38, 96, 277, 1421, 2464, 6654, 61802, 293298, 977440, 3457374, 15961755, 68638807, 261722656, 993323854, 4081202724, 16722068344, 65831346572, 256639112606, 1025719342194, 4118393609362, 16324710723952
Offset: 0

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A047149 T(2n,n), array T as in A047140.

Original entry on oeis.org

1, 3, 13, 68, 395, 2383, 14628, 91002, 572629, 3635105, 23230955, 149252778, 963125552, 6238012172, 40529533578, 264038158806, 1724159758595, 11281813669783, 73955009216581, 485575827838870, 3192818972511443
Offset: 0

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Clark Kimberling. Definition revised Dec 08 2006

Keywords

A047130 Array read by descending antidiagonals: T(h,k) is the number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and no up-step crosses the line y = 3x/4. (Thus a path crosses the line only at lattice points and on right-steps.)

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 1, 4, 5, 5, 4, 1, 1, 5, 9, 5, 9, 5, 1, 1, 6, 14, 14, 14, 14, 6, 1, 1, 7, 20, 28, 28, 28, 20, 7, 1, 1, 8, 27, 48, 56, 28, 48, 27, 8, 1, 1, 9, 35, 75, 104, 84, 76, 75, 35, 9, 1, 1, 10, 44, 110, 179, 188, 84
Offset: 0

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Author

Clark Kimberling. Definition revised Dec 08 2006

Keywords

Examples

			Array begins:
===================================
h\k | 0 1  2  3   4   5   6   7
----+------------------------------
  0 | 1 1  1  1   1   1   1   1 ...
  1 | 1 1  2  3   4   5   6   7 ...
  2 | 1 2  2  5   9  14  20  27 ...
  3 | 1 3  5  5  14  28  48  75 ...
  4 | 1 4  9 14  28  56 104 179 ...
  5 | 1 5 14 28  28  84 188 367 ...
  6 | 1 6 20 48  76  84 272 639 ...
  7 | 1 7 27 75 151 235 272 911 ...
  ...
		

Crossrefs

Programs

  • PARI
    A(h, k=h)={my(M=matrix(h+1, k+1, i, j, 1)); for(h=1, h, for(k=1, k, M[1+h, 1+k] = M[h, 1+k] + if(4*k>3*h && 4*(k-1)<3*h, 0, M[1+h, k]))); M}
    { my(T=A(10)); for(i=1, #T, print(T[i, ]))} \\ Andrew Howroyd, Jan 19 2020
Showing 1-10 of 10 results.