A090019 -id:A090019 - cp's OEIS frontend

A067410 Triangle with columns built from certain power sequences.

1, 2, 1, 4, 3, 1, 8, 12, 4, 1, 16, 48, 24, 5, 1, 32, 192, 144, 40, 6, 1, 64, 768, 864, 320, 60, 7, 1, 128, 3072, 5184, 2560, 600, 84, 8, 1, 256, 12288, 31104, 20480, 6000, 1008, 112, 9, 1, 512, 49152, 186624, 163840, 60000, 12096, 1568, 144, 10, 1

Offset: 0

Wolfdieter Lang, Jan 25 2002

			Triangle starts:
  1;
  2,  1;
  4,  3, 1;
  8, 12, 4, 1;
  ...

Indranil Ghosh, Rows 0..125, flattened

Cf. A009998 (triangle built from powers of (m+1)), A067402.

Columns m=0..8 are A000079, A002001, A067411, A067412, A090019, A067413, A067414, A067415, A067416.

A[n_,m_]:=If[n==m,1,(m+2)(2(m+1))^(n-m-1)]; Flatten[Table[A[n,m],{n,0,9},{m,0,n}]] (* Stefano Spezia, Sep 30 2022 *)

a(n, m) = 1 if n = m; a(n, m) = (m+2)*(2*(m+1))^(n-m-1) if n > m >= 0.

G.f. for column m: (x^m)*(1-m*x)/(1-2*(m+1)*x).

A326811 Numbers in A326806 whose sum of digits is not a power of 10 and are not of the form 510^k or 610^k.

Original entry on oeis.org

0, 6667, 58824, 8823529412, 5263157894737, 19607843137255, 65217391304348, 98360655737705, 746268656716418, 4761904761904762, 8955223880597015, 58823529411764706, 1369863013698630137, 60240963855421686747, 3061224489795918367347, 34090909090909090909091

Offset: 1

Chai Wah Wu, Oct 19 2019

A326806 = A326811 UNION A326833 UNION A090019 UNION A093143. Note that several terms (e.g. a(10), a(13), a(17)-a(19)) look like the rounding off of a periodic sequence, i.e. yxxxa9xxxa9xxxa9... rounded off to yxxxa9xxxa9xxxb, where b = a+1. Perhaps these can be considered near-cyclic numbers? - Chai Wah Wu, Oct 21 2019

Giovanni Resta, Table of n, a(n) for n = 1..70 (first 19 terms from Chai Wah Wu)

Cf. A326806, A326833, A090019, A093143.

More terms from Chai Wah Wu, Oct 21 2019

A346178 Expansion of (1-2x)/(1-10x).

Original entry on oeis.org

1, 8, 80, 800, 8000, 80000, 800000, 8000000, 80000000, 800000000, 8000000000, 80000000000, 800000000000, 8000000000000, 80000000000000, 800000000000000, 8000000000000000, 80000000000000000, 800000000000000000, 8000000000000000000, 80000000000000000000

Offset: 0

Felix Fröhlich, Jul 09 2021

Index entries for linear recurrences with constant coefficients, signature (10).

Cf. expansion of (1-k*x)/(1-10*x) A011557 (k=0), A196662 (k=3), A090019 (k=4), A093143 (k=5), A093141 (k=6), A093138 (k=7), A093136 (k=8).

PARI
```
Vec((1-2*x)/(1-10*x) + O(x^20))
```

a(n) = 8*10^(n-1), n>0.

E.g.f.: (1 + 4*exp(10*x))/5. - Stefano Spezia, Jul 09 2021

cp's OEIS Frontend

A067410 Triangle with columns built from certain power sequences.

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A326811 Numbers in A326806 whose sum of digits is not a power of 10 and are not of the form 510^k or 610^k.

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A346178 Expansion of (1-2x)/(1-10x).

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Keywords

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PARI

Formula

cp's OEIS Frontend

A067410 Triangle with columns built from certain power sequences.

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Author

Keywords

Examples

Links

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Programs

Mathematica

Formula

A326811 Numbers in A326806 whose sum of digits is not a power of 10 and are not of the form 5*10^k or 6*10^k.

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Author

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Comments

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Extensions

A346178 Expansion of (1-2*x)/(1-10*x).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A326811 Numbers in A326806 whose sum of digits is not a power of 10 and are not of the form 510^k or 610^k.

A346178 Expansion of (1-2x)/(1-10x).