A048474 -id:A048474 - cp's OEIS frontend

A049513 Array T by antidiagonals: T(k,n) = kn2^(n-1) + 1, n >= 0, k >= 0.

1, 1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 4, 9, 13, 1, 1, 5, 13, 25, 33, 1, 1, 6, 17, 37, 65, 81, 1, 1, 7, 21, 49, 97, 161, 193, 1, 1, 8, 25, 61, 129, 241, 385, 449, 1, 1, 9, 29, 73, 161, 321, 577, 897, 1025, 1, 1, 10, 33, 85, 193, 401, 769, 1345, 2049, 2305, 1, 1, 11, 37, 97, 225, 481

Offset: 0

Michael Somos, Sep 25 1999

			Antidiagonals: 1; 1,1; 1,2,1; 1,3,5,1; 1,4,9,13,1; ...

Cf. A000337, A002064, A005183, A016813, A017533, A048474, A049069, A048472.

Essentially the same as A049069.

PARI
```
{T(k, n) = k * n * 2^(n-1) + 1}
```

A005183(n) = T(1, n), A002064(n) = T(2, n), A048474(n) = T(3, n), A000337(n) = T(4, n), A016813(n) = T(n, 2), A017533(n) = T(n, 3).

A086090 2^n+n3^n.

Original entry on oeis.org

1, 5, 22, 89, 340, 1247, 4438, 15437, 52744, 177659, 591514, 1950665, 6381388, 20734391, 66977950, 215266373, 688813072, 2195513843, 6973830946, 22083492161, 69736736596, 219669514415, 690387505702, 2165301501629

Offset: 0

Paul Barry, Jul 09 2003

Binomial transform of A048474

Index entries for linear recurrences with constant coefficients, signature (8,-21,18).

Cf. A086091.

Table[2^n+n*3^n,{n,0,30}] (* or *) LinearRecurrence[{8,-21,18},{1,5,22},30] (* Harvey P. Dale, Jun 06 2017 *)

G.f.: (1-3x+3x^2)/((1-2x)(1-3x)^2)

A134232 A007318 * M, where M = triangle in which row n consists of n-1 zeros followed by 2n-1, n+1.

Original entry on oeis.org

1, 2, 2, 3, 7, 3, 4, 15, 14, 4, 5, 26, 38, 23, 5, 6, 40, 80, 75, 34, 6, 7, 57, 145, 185, 129, 47, 7, 8, 77, 238, 385, 364, 203, 62, 8, 0, 9, 100, 364, 714, 854, 644, 300, 79, 9, 10, 126, 528, 1218, 1764, 1680, 1056, 423, 98, 10

Offset: 0

Gary W. Adamson, Oct 14 2007

Row sums = A048474: (1, 4, 13, 37, 97, 241, 577, ...).

			First few rows of the triangle:
  1;
  2,  2;
  3,  7,   3;
  4, 15,  14,   4;
  5, 26,  38,  23,   5;
  6, 40,  80,  75,  34,  6;
  7, 57, 145, 185, 129, 47, 7;
  ...

Cf. A048474.

Binomial transform of an infinite lower triangular matrix with rows = (n-1) zeros followed by (2n-1), (n+1). A007318 * an infinite lower triangular matrix with (1,2,3,...) in the main diagonal, (1,3,5,...) in the subdiagonal and the rest zeros.

cp's OEIS Frontend

A049513 Array T by antidiagonals: T(k,n) = kn2^(n-1) + 1, n >= 0, k >= 0.

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PARI

Formula

A086090 2^n+n3^n.

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Mathematica

Formula

A134232 A007318 * M, where M = triangle in which row n consists of n-1 zeros followed by 2n-1, n+1.

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Author

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Comments

Examples

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Formula

cp's OEIS Frontend

A049513 Array T by antidiagonals: T(k,n) = k*n*2^(n-1) + 1, n >= 0, k >= 0.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

Formula

A086090 2^n+n3^n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A134232 A007318 * M, where M = triangle in which row n consists of n-1 zeros followed by 2n-1, n+1.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

A049513 Array T by antidiagonals: T(k,n) = kn2^(n-1) + 1, n >= 0, k >= 0.