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A243860 2^(n+1) - (n-1)^2. 1
1, 4, 7, 12, 23, 48, 103, 220, 463, 960, 1967, 3996, 8071, 16240, 32599, 65340, 130847, 261888, 523999, 1048252, 2096791, 4193904, 8388167, 16776732, 33553903, 67108288, 134217103, 268434780, 536870183, 1073741040, 2147482807, 4294966396, 8589933631, 17179868160, 34359737279, 68719475580 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sequences of the form (k-1)^m - m^(k+1):

k\m | 0 |  1 |     2 |       3 |         4 |          5 |           6 |

-----------------------------------------------------------------------

0   | 1 | -2 |    -1 |      -4 |        -3 |         -6 |          -5 |

1   | 1 | -1 |    -4 |      -9 |       -16 |        -25 |         -36 |

2   | 1 |  0 |    -7 |     -26 |       -63 |       -124 |        -215 |

3   | 1 |  1 |   -12 |     -73 |      -240 |       -593 |       -1232 |

4   | 1 |  2 |   -23 |    -216 |      -943 |      -2882 |       -7047 |

5   | 1 |  3 |   -43 |    -665 |     -3840 |     -14601 |      -42560 |

6   | 1 |  4 |  -103 |   -2062 |    -15759 |     -75000 |     -264311 |

7   | 1 |  5 |  -220 |   -6345 |    -64240 |    -382849 |    -1632960 |

8   | 1 |  6 |  -463 |  -19340 |   -259743 |   -1936318 |    -9960047 |

9   | 1 |  7 |  -960 |  -58537 |  -1044480 |   -9732857 |   -60204032 |

10  | 1 |  8 | -1967 | -176418 |  -4187743 |  -48769076 |  -362265615 |

11  | 1 |  9 | -3996 | -530441 | -16767216 | -244040625 | -2175782336 |

LINKS

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

FORMULA

a(n) = 5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4). - Colin Barker, Jun 12 2014

G.f.: (6*x^3-4*x^2-x+1) / ((x-1)^3*(2*x-1)). - Colin Barker, Jun 12 2014

EXAMPLE

1 = 2^(0+1) - (0-1)^2, 4 = 2^(1+1) - (1-1)^2, 7 = 2^(2+1) - (2-1)^2.

MAPLE

A243860:=n->2^(n + 1) - (n - 1)^2; seq(A243860(n), n=0..30); # Wesley Ivan Hurt, Jun 12 2014

MATHEMATICA

Table[2^(n + 1) - (n - 1)^2, {n, 0, 30}] (* Wesley Ivan Hurt, Jun 12 2014 *)

LinearRecurrence[{5, -9, 7, -2}, {1, 4, 7, 12}, 40] (* Harvey P. Dale, Nov 29 2015 *)

PROG

(MAGMA) [2^(n+1) - (n-1)^2: n in [0..35]];

(PARI) Vec((6*x^3-4*x^2-x+1)/((x-1)^3*(2*x-1)) + O(x^100)) \\ Colin Barker, Jun 12 2014

CROSSREFS

Sequences of the form (k-1)^m - m^(k+1): A000012 (m = 0), A023444 (m = 1), (-1)*(this sequence) for m = 2, A114285 (k = 0),(A000007-A000290) for k = 1, A024001 (k = 2), A024014 (k = 3), A024028 (k = 4), A024042 (k = 5), A024056 (k = 6), A024070 (k = 7), A024084 (k = 8), A024098 (k = 9), A024112 (k = 10), A024126 (k = 11).

Sequence in context: A023624 A123194 A208668 * A322619 A299900 A215329

Adjacent sequences:  A243857 A243858 A243859 * A243861 A243862 A243863

KEYWORD

nonn,easy

AUTHOR

Juri-Stepan Gerasimov, Jun 12 2014

STATUS

approved

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Last modified June 17 13:59 EDT 2021. Contains 345083 sequences. (Running on oeis4.)