A047130 -id:A047130 - cp's OEIS frontend

A047131 a(n) = Sum_{i=0..n} A047130(i, n-i).

1, 2, 3, 6, 10, 20, 35, 70, 140, 252, 504, 932, 1864, 3493, 6986, 13972, 26265, 52530, 100168, 200336, 384573, 769146, 1538292, 2950530, 5901060, 11422700, 22845400, 44403564, 88807128, 177614256, 344644881, 689289762, 1346117062

Offset: 0

Clark Kimberling

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..200

Cf. A047130.

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}
seq(n)={my(T=A(n)); vector(#T, k, sum(i=0, k-1, T[1+i, k-i]))} \\ Andrew Howroyd, Jan 19 2020

Definition corrected and edited by Georg Fischer, Jan 19 2020

A047132 T(n,n), array T as in A047130.

Original entry on oeis.org

1, 1, 2, 5, 28, 84, 272, 911, 3885, 14049, 50891, 185464, 735146, 2794719, 10565837, 39940553, 155711860, 601589056, 2317413464, 8920255482, 34742183340, 135196049411, 525683426601, 2043377119966, 7980296279061

Offset: 0

Clark Kimberling

nonn

Definition corrected by Georg Fischer, Jan 20 2020

A047133 T(n,n-1), array T as in A047130.

Original entry on oeis.org

1, 2, 5, 14, 28, 84, 272, 1679, 5564, 19613, 70504, 311534, 1172750, 4405073, 16581264, 67108040, 260573610, 1004778126, 3867996120, 15289911196, 59854486782, 233437968413, 909025875014, 3575067252387, 14038457059264

Offset: 1

Clark Kimberling

nonn

Definition corrected by Georg Fischer, Jan 20 2020

A047134 T(n,n-2), array T as in A047130.

Original entry on oeis.org

1, 3, 9, 28, 76, 235, 768, 1679, 5564, 19613, 126070, 437604, 1610354, 6015427, 27167487, 104861750, 403189070, 1550582656, 6369655714, 25112303442, 98241919002, 383342448413, 1531690132421, 6058160780203, 23859853900666

Offset: 2

Clark Kimberling

nonn

Definition corrected by Georg Fischer, Jan 20 2020

A047135 a(n) = T(n,n-3), array T as in A047130.

Original entry on oeis.org

1, 4, 14, 48, 151, 496, 1679, 4892, 16099, 55566, 126070, 437604, 1610354, 10586223, 37753710, 142615460, 545804530, 2501659594, 9822392246, 38387432220, 149904480000, 622664257407, 2483093527816, 9821396841402

Offset: 3

Clark Kimberling

nonn

Cf. A047130.

Definition corrected by Georg Fischer, Jan 20 2020

A047136 a(n) = T(n,n+1), array T as in A047130.

Original entry on oeis.org

1, 2, 5, 14, 56, 188, 639, 2206, 8485, 31278, 114960, 423612, 1621969, 6160764, 23359289, 88603820, 341015446, 1312635338, 5052259362, 19452272144, 75341562629, 292245458188, 1134351244952, 4405229026674, 17153557736343

Offset: 0

Clark Kimberling

nonn

Cf. A047130.

Definition corrected by Georg Fischer, Jan 20 2020

A047137 a(n) = T(n,n+2), array T as in A047130.

Original entry on oeis.org

1, 3, 9, 28, 104, 367, 1295, 4600, 17229, 64069, 238148, 886823, 3366045, 12793452, 48663267, 185303586, 711046282, 2734845898, 10532016662, 40599379289, 157049408777, 608667818351, 2361851906708, 9173261457282

Offset: 0

Clark Kimberling

nonn

Cf. A047130.

Definition corrected by Georg Fischer, Jan 20 2020

A047138 a(n) = T(n,n+3), array T as in A047130.

Original entry on oeis.org

1, 4, 14, 48, 179, 656, 2394, 8744, 32791, 123188, 463211, 1744076, 6632688, 25303978, 96699766, 370030836, 1422210560, 5479757300, 21147107145, 81707846148, 316422360163, 1227500661756, 4768032430608, 18539704936398

Offset: 0

Clark Kimberling

nonn

Cf. A047130.

Definition corrected by Georg Fischer, Jan 20 2020

A047139 T(2n,n), array T as in A047130.

Original entry on oeis.org

1, 2, 9, 48, 261, 1534, 9319, 56808, 353362, 2227380, 14099553, 89931668, 577292621, 3718701300, 24047442913, 156059054586, 1015345651345, 6621929417524, 43283675452318, 283439130488986, 1859169844171611

Offset: 0

Clark Kimberling. Definition revised Dec 08 2006

nonn

A047140 Array read by diagonals: T(h,k)=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=4x/3. (Thus a path crosses the line only at lattice points and on right-steps.).

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 4, 4, 1, 1, 3, 2, 8, 5, 1, 1, 4, 5, 10, 13, 6, 1, 1, 5, 9, 15, 23, 19, 7, 1, 1, 6, 14, 24, 38, 42, 26, 8, 1, 1, 7, 20, 38, 62, 80, 68, 34, 9, 1, 1, 8, 27, 58, 38, 142, 148, 102, 43, 10, 1, 1, 9, 35, 85, 96, 180, 290

Offset: 0

Clark Kimberling. Definition revised Dec 08 2006

			Array begins:
======================================
h\k | 0 1  2   3   4   5    6    7
----+---------------------------------
  0 | 1 1  1   1   1   1    1    1 ...
  1 | 1 2  1   2   3   4    5    6 ...
  2 | 1 3  4   2   5   9   14   20 ...
  3 | 1 4  8  10  15  24   38   58 ...
  4 | 1 5 13  23  38  62   38   96 ...
  5 | 1 6 19  42  80 142  180   96 ...
  6 | 1 7 26  68 148 290  470  566 ...
  7 | 1 8 34 102 250 540 1010 1576 ...
  ...

Andrew Howroyd, Table of n, a(n) for n = 0..1325

Cf. A047141, A047142, A047143, A047144, A047145, A047146, A047147, A047148, A047149.

Cf. A047110, A047130, A047150.

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

cp's OEIS Frontend

A047131 a(n) = Sum_{i=0..n} A047130(i, n-i).

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A047132 T(n,n), array T as in A047130.

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A047133 T(n,n-1), array T as in A047130.

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A047134 T(n,n-2), array T as in A047130.

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A047135 a(n) = T(n,n-3), array T as in A047130.

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A047136 a(n) = T(n,n+1), array T as in A047130.

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A047137 a(n) = T(n,n+2), array T as in A047130.

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Extensions

A047138 a(n) = T(n,n+3), array T as in A047130.

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Extensions

A047139 T(2n,n), array T as in A047130.

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Author

Keywords

A047140 Array read by diagonals: T(h,k)=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=4x/3. (Thus a path crosses the line only at lattice points and on right-steps.).

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Examples

Links

Crossrefs

Programs

PARI