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 1-3 of 3 results.

A086351 T(n,3) of A086350.

Original entry on oeis.org

1, 4, 17, 74, 325, 1432, 6317, 27878, 123049, 543148, 2397545, 10583234, 46716589, 206216896, 910285253, 4018193246, 17737162705, 78295623508, 345613602113, 1525612248122, 6734378273941, 29726983906792, 131221255523165
Offset: 0

Views

Author

Paul Barry, Jul 18 2003

Keywords

Comments

Binomial transform of A007052. Second binomial transform of Pell numbers A000129 (without leading zero).

Links

Programs

  • PARI
    a(n)=my(sqrt2=quadgen(8)); simplify(((1+sqrt2)*(3+sqrt2)^n-(1-sqrt2)*(3-sqrt2)^n)/sqrt2^3) \\ Charles R Greathouse IV, Oct 24 2014

Formula

G.f.: (1-2x)/(1-6x+7x^2);
a(n)=((1+sqrt(2))(3+sqrt(2))^n-(1-sqrt(2))(3-sqrt(2))^n)/(sqrt(8)).
a(n) = A081179(n+1)-2*A081179(n). - R. J. Mathar, Dec 05 2022

A086352 Main diagonal of square array A086350.

Original entry on oeis.org

1, 2, 10, 74, 740, 9354, 143144, 2573586, 53180944, 1242078802, 32358633632, 930370449370, 29264294868544, 999646208968666, 36852747307934336, 1458402092927302178, 61665517131334975744, 2774522039432235946914
Offset: 0

Views

Author

Paul Barry, Jul 18 2003

Keywords

Crossrefs

Cf. A000169, A086350.

Formula

a(n) = ((1+sqrt(2))*(n+sqrt(2))^n-(1-sqrt(2))*(n-sqrt(2))^n)/sqrt(8).

A086404 Square array of numbers T(n,k) = ((1+sqrt(3))*(k+sqrt(3))^n-(1-sqrt(3))*(k-sqrt(3))^n)/(2*sqrt(3)), read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 1, 3, 6, 3, 1, 4, 11, 16, 9, 1, 5, 18, 41, 44, 9, 1, 6, 27, 84, 153, 120, 27, 1, 7, 38, 151, 396, 571, 328, 27, 1, 8, 51, 248, 857, 1872, 2131, 896, 81, 1, 9, 66, 381, 1644, 4893, 8856, 7953, 2448, 81, 1, 10, 83, 556, 2889, 10984, 28003, 41904, 29681
Offset: 0

Views

Author

Paul Barry, Jul 19 2003

Keywords

Examples

			Rows begin
  1, 1,  3,   3,   9, ...
  1, 2,  6,  16,  44, ...
  1, 3, 11,  41, 153, ...
  1, 4, 18,  84, 396, ...
  1, 5, 27, 151, 857, ...

Crossrefs

Rows include A002605, A079935, A086405. Main diagonal is A086406. Rows are successive binomial transforms of (1, 1, 3, 3, 9, 9, ...).
Cf. A086350.
Showing 1-3 of 3 results.

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

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