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.

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A217764 Array defined by a(n,k) = floor((k+2)/2)*3^n - floor((k+1)/2)*2^n, read by antidiagonals.

Original entry on oeis.org

1, 3, 0, 9, 1, 1, 27, 5, 4, 0, 81, 19, 14, 2, 1, 243, 65, 46, 10, 5, 0, 729, 211, 146, 38, 19, 3, 1, 2187, 665, 454, 130, 65, 15, 6, 0, 6561, 2059, 1394, 422, 211, 57, 24, 4, 1, 19683, 6305, 4246, 1330, 665, 195, 84, 20, 7, 0, 59049, 19171, 12866, 4118, 2059, 633, 276, 76, 29, 5, 1
Offset: 0

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Author

Ross La Haye, Mar 23 2013

Keywords

Comments

Columns 0,1,2,3 respectively correspond to relations R_3, R_4, R_0, R_1 defined in La Haye paper listed below.

Examples

			a(4,4) = 211 because floor((4+2)/2)*3^4 - floor((4+1)/2)*2^4 = 3*3^4 - 2*2^4 = 243 - 32 = 211.

Links

Crossrefs

Cf. a(1,k) = A084964(k+2); a(n,0) = A000244(n); a(n,1) = A001047(n); a(n,2) = A027649(n); a(n,3) = A056182(n); a(n,4) = A001047(n+1); a(n,5) = A210448(n); a(n,6) = A166060(n); a(n,7) = A145563(n); a(n,8) = A102485(n).

Formula

a(n,k) = floor((k+2)/2)*3^n - floor((k+1)/2)*2^n. a(n,k) = 5*a(n-1,k) - 6*a(n-2,k); a(0,k) = floor((k+2)/2) - floor((k+1)/2), a(1,k) = floor((k+2)/2)*3 - floor((k+1)/2)*2.

A169650 a(1) = 3; thereafter a(n) = 3*a(n-1)+2^n-6.

Original entry on oeis.org

3, 7, 23, 79, 263, 847, 2663, 8239, 25223, 76687, 232103, 700399, 2109383, 6344527, 19066343, 57264559, 171924743, 516036367, 1548633383, 4646948719, 13942943303, 41833024207, 125507461223, 376539160879, 1129651037063, 3389020220047, 10167194877863
Offset: 1

Views

Author

N. J. A. Sloane, Apr 07 2010

Keywords

Links

Crossrefs

Apart from offset, equals A145563 + 3. Arises in analyzing A169648.

Programs

  • Maple
    a:=n->if n=1 then 3 else 3*a(n-1)+2^n-6; fi;
  • Mathematica
    a[n_Integer/;n>=1]:=4*3^(n-1)-2^(n+1)+3 (* Todd Silvestri, Dec 15 2014 *)
RecurrenceTable[{a[1]==3,a[n]==3a[n-1]+2^n-6},a,{n,30}] (* Harvey P. Dale, Jan 22 2018 *)

Formula

a(n) = 4*3^(n-1)-2^(n+1)+3. - Todd Silvestri, Dec 15 2014
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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