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 1-2 of 2 results.

A133600 Row sums of triangle A133599.

Original entry on oeis.org

1, 4, 7, 16, 28, 64, 112, 256, 448, 1024, 1792, 4096, 7168, 16384, 28672, 65536, 114688, 262144, 458752, 1048576, 1835008, 4194304, 7340032, 16777216, 29360128, 67108864, 117440512, 268435456, 469762048, 1073741824, 1879048192
Offset: 1

Views

Author

Gary W. Adamson, Sep 18 2007

Keywords

Examples

			a(4) = 16 = sum of row 4 terms of triangle A133599 = (3 + 7 + 5 + 1).
a(4) = 16 = 2^4.
a(7) = 112 = 7 * 2^4 = 7 * 16.

Links

Crossrefs

Cf. A133599, A000302 (bisection), A002042 (bisection, n>2).

Programs

  • Mathematica
    LinearRecurrence[{0,4},{1,4,7},40] (* Harvey P. Dale, Jan 12 2020 *)
  • PARI
    {vector(31, n, if(n==1, 1, if(n%2>0, 7*2^(n-3), 2^n)))} /* Klaus Brockhaus, Nov 26 2009 */

Formula

For even-indexed terms, a(n) = 2^n. For odd-indexed terms, a(n) = 7 * 2^(n-3).
G.f.: -x*(x+1)*(3*x+1)/(2*x-1)/(2*x+1). - R. J. Mathar, Nov 14 2007
a(n) = 4*a(n-2) for n > 3; a(1) = 1, a(2) = 4, a(3) = 7. - Klaus Brockhaus, Nov 26 2009

A171475 a(n) = 6*a(n-1) - 8*a(n-2), for n > 2, with a(0) = 1, a(1) = 6, a(2) = 27.

Original entry on oeis.org

1, 6, 27, 114, 468, 1896, 7632, 30624, 122688, 491136, 1965312, 7862784, 31454208, 125822976, 503304192, 2013241344, 8053014528, 32212156416, 128848822272, 515395682304, 2061583515648, 8246335635456, 32985345687552
Offset: 0

Views

Author

Klaus Brockhaus, Dec 09 2009

Keywords

Comments

Binomial transform of A037480; second binomial transform of A133600.
First differences of A080960.

Links

Crossrefs

Cf. A037480 ((5*3^n +(-1)^n -6)/8), A133600 (row sums of triangle A133599), A080960 (third binomial transform of A010685).

Programs

  • Magma
    I:=[6,27]; [1] cat [n le 2 select I[n] else 6*Self(n-1) - 8*Self(n-2): n in [1..30]]; // G. C. Greubel, Dec 02 2021
  • Mathematica
    Table[If[n==0, 1, 3*(5*4^n - 2*2^n)/8],{n,0,30}] (* G. C. Greubel, Dec 02 2021 *)
LinearRecurrence[{6,-8},{1,6,27},30] (* Harvey P. Dale, Oct 25 2023 *)
  • PARI
    {m=21; v=concat([1, 6, 27], vector(m-3)); for(n=4, m, v[n]=6*v[n-1]-8*v[n-2]); v}
  • Sage
    [1]+[3*(5*4^n - 2*2^n)/8 for n in (1..30)] # G. C. Greubel, Dec 02 2021

Formula

a(n) = 3*(5*4^n - 2*2^n)/8 for n > 0.
G.f.: (1-x)*(1+x)/((1-2*x)*(1-4*x)).
E.g.f.: (1/8)*(-1 - 6*exp(2*x) + 15*exp(4*x)). - G. C. Greubel, Dec 02 2021
Showing 1-2 of 2 results.

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

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