A023054 Simon Plouffe's conjectured extension of sequence A008368.

1, 1, 3, 4, 7, 8, 13, 14, 20, 22, 29, 31, 40, 42, 52, 55, 66, 69, 82, 85, 99, 103, 118, 122, 139, 143, 161, 166, 185, 190, 211, 216, 238, 244, 267, 273, 298, 304, 330, 337, 364, 371, 400, 407, 437, 445, 476, 484, 517, 525, 559, 568, 603, 612, 649, 658, 696, 706, 745, 755

Offset

0,3

Links

Table of n, a(n) for n=0..59.

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

Index entries for linear recurrences with constant coefficients, signature (0,2,1,-1,-2,0,1).

Formula

G.f.: (1-x^5)/((1-x)*(1-x^2)^2*(1-x^3)).

Euler transform of length 5 sequence [ 1, 2, 1, 0, -1]. - Michael Somos, May 22 2014

a(-3 - n) = a(n). - Michael Somos, May 22 2014

a(2*n + 2) - a(2*n) = A032793(n + 2). a(2*n + 3) - a(2*n + 1) = A042706(n + 2). - Michael Somos, May 22 2014

Example

G.f. = 1 + x + 3*x^2 + 4*x^3 + 7*x^4 + 8*x^5 + 13*x^6 + 14*x^7 + 20*x^8 + ...

Mathematica

CoefficientList[Series[(1-x^5)/((1-x)*(1-x^2)^2*(1-x^3)), {x, 0, 59}], x] (* Georg Fischer, Oct 13 2020 *)

Prog

(PARI) {a(n) = if( n%2, (n + 1) * (5*n + 7) + 8 * (n%6 == 3), (n + 2) * (5*n + 8) + 8 * (n%6 == 0) ) / 24}; /* Michael Somos, May 22 2014 */
(PARI) {a(n) = if( n<0, n = -3 - n); polcoeff( (1 - x^5) / ((1 - x) * (1 - x^2)^2 * (1 - x^3)) + x * O(x^n), n)}; /* Michael Somos, May 22 2014 */

Crossrefs

Cf. A032793, A042706.

Sequence in context: A284506 A157419 A008368 * A060023 A345531 A357644

Adjacent sequences: A023051 A023052 A023053 * A023055 A023056 A023057

Keyword

nonn,easy

Author

N. J. A. Sloane and J. H. Conway

Status

approved