|
| |
|
|
A014616
|
|
a(n) = solution to the postage stamp problem with 2 denominations and n stamps.
|
|
28
| |
|
|
2, 4, 7, 10, 14, 18, 23, 28, 34, 40, 47, 54, 62, 70, 79, 88, 98, 108, 119, 130, 142, 154, 167, 180, 194, 208, 223, 238, 254, 270, 287, 304, 322, 340, 359, 378, 398, 418, 439, 460, 482, 504, 527, 550, 574, 598, 623, 648, 674, 700, 727, 754, 782, 810, 839, 868
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Lunnon defines "solution" to be the smallest value not obtainable by the best set of stamps. The solutions given are one lower than this, that is, the sequence gives the largest number obtainable without a break using the best set of stamps.
|
|
|
REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, C12.
W. F. Lunnon, A postage stamp problem. Comput. J. 12 (1969) 377-380.
Amitabha Tripathi, A Note on the Postage Stamp Problem, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.3.
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Erich Friedman, Postage stamp problem
Eric Weisstein's World of Mathematics, Postage stamp problem
Hugh Thomas and Stephanie van Willigenburg, Compact symmetric solutions to the postage stamp problem arXiv:0706.3250
Index to sequences with linear recurrences with constant coefficients, signature (2,0,-2,1)
|
|
|
FORMULA
| a(n) = floor((n^2 + 6*n + 1)/4).
a(n) = A002620(n+3)-2 = (2*n*(n+6)-(-1)^n+1)/8.
G.f. x*(-2+x^2) / ( (1+x)*(x-1)^3 ). - R. J. Mathar, Jul 09 2011
|
|
|
MATHEMATICA
| a[n_?OddQ] := (n^2 + 6*n + 1)/4; a[n_?EvenQ] := n*(n + 6)/4; Table[a[n], {n, 1, 56}] (* From Jean-François Alcover, Dec 14 2011, after first formula *)
|
|
|
PROG
| (MAGMA) [(2*n*(n+6)-(-1)^n+1)/8: n in [1..60]]; // Vincenzo Librandi, Jul 09 2011
|
|
|
CROSSREFS
| Equals A024206 - 1.
Postage stamp sequences: A001208 A001209 A001210 A001211 A001212 A001213 A001214 A001215 A001216 A005342 A005343 A005344 A014616 A053346 A053348 A075060 A084192 A084193
A row or column of the array A196416 (possibly with 1 subtracted from it).
Sequence in context: A130251 A088236 A194244 * A184674 A183136 A144873
Adjacent sequences: A014613 A014614 A014615 * A014617 A014618 A014619
|
|
|
KEYWORD
| nonn,nice,easy
|
|
|
AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
|
|
|
EXTENSIONS
| Entry improved by comments from John Seldon (johnseldon(AT)onetel.com), Sep 15 2004
More terms from John W. Layman (layman(AT)math.vt.edu), Apr 13 1999
|
| |
|
|
