A151977 Numbers that are congruent to {0, 1} mod 16.

0, 1, 16, 17, 32, 33, 48, 49, 64, 65, 80, 81, 96, 97, 112, 113, 128, 129, 144, 145, 160, 161, 176, 177, 192, 193, 208, 209, 224, 225, 240, 241, 256, 257, 272, 273, 288, 289, 304, 305, 320, 321, 336, 337, 352, 353, 368, 369, 384, 385, 400, 401, 416, 417, 432, 433, 448, 449

Offset

1,3

Comments

Numbers k such that k^2 - k is divisible by 16.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(k)=2^(k+3) for k > 0; {b(n)} = 1,16,32,64,128,256,... - Philippe Deléham, Oct 17 2011

G.f.: x^2*(1+15*x)/((1+x)*(1-x)^2). - Vincenzo Librandi, Jul 11 2012

a(n) = (32*n - 14*(-1)^n - 46)/4. - Vincenzo Librandi, Jul 11 2012

From David Lovler, Aug 18 2022: (Start)

a(n) = A321212(n) - 2.

a(n) = a(n-2) + 16.

E.g.f.: 15 + ((16*x - 23)*exp(x) - 7*exp(-x))/2. (End)

Mathematica

CoefficientList[Series[x*(1+15*x)/((1+x)(1-x)^2), {x, 0, 60}], x] (* Vincenzo Librandi, Jul 11 2012 *)
LinearRecurrence[{1, 1, -1}, {0, 1, 16}, 80] (* Harvey P. Dale, Jul 24 2021 *)

Prog

(PARI) forstep(n=0, 200, [1, 15], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
(PARI) a(n) = (16*n - 7*(-1)^n - 23)/2 \\ David Lovler, Aug 18 2022
(Magma) [(32*n-14*(-1)^n-46)/4: n in [1..60]]; // Vincenzo Librandi, Jul 11 2012

Crossrefs

Cf. A321212.

Sequence in context: A007636 A241751 A244431 * A252492 A319281 A022106

Adjacent sequences: A151974 A151975 A151976 * A151978 A151979 A151980

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 23 2009

Status

approved