A167814 -id:A167814 - cp's OEIS frontend

A167809 Number of admissible bases in the postage stamp problem for n denominations and h = 2 stamps.

1, 2, 5, 17, 65, 292, 1434, 7875, 47098, 305226, 2122983, 15752080, 124015310, 1031857395, 9041908204, 83186138212, 801235247145, 8059220936672, 84463182889321

Offset: 1

Yogy Namara (yogy.namara(AT)gmail.com), Nov 12 2009

A basis 1 = b_1 < b_2 ... < b_n is admissible if all the values 1 <= x <= b_n are obtainable as a sum of at most h (not necessarily distinct) numbers in the basis.

Conjecture: a(n) >= A000108(n). - Michael Chu, May 16 2022

R. K. Guy, Unsolved Problems in Number Theory, C12.

R. Alter and J. A. Barnett, A postage stamp problem, Amer. Math. Monthly, 87 (1980), 206-210.
M. F. Challis, Two new techniques for computing extremal h-bases A_k, Comp J 36(2) (1993) 117-126
Erich Friedman, Postage stamp problem
J. Kohonen, A meet-in-the-middle algorithm for finding extremal restricted additive 2-bases, arXiv preprint arXiv:1403.5945 [math.NT], 2014 and J. Int. Seq. 17 (2014) # 14.6.8.
J. Kohonen, Early Pruning in the Restricted Postage Stamp Problem, arXiv preprint arXiv:1503.03416 [math.NT], 2015.
W. F. Lunnon, A postage stamp problem, Comput. J. 12 (1969) 377-380.
S. Mossige, Algorithms for Computing the h-Range of the Postage Stamp Problem, Math. Comp. 36 (1981) 575-582.

Other enumerations with different parameters: A167809 (h = 2), A167810 (h = 3), A167811 (h = 4), A167812 (h = 5), A167813 (h = 6), A167814 (h = 7).

For h = 2, cf. A008932.

a(17) from simple depth-first search by Jukka Kohonen, Jun 16 2016

a(18)-a(19) from depth-first search by Jukka Kohonen, Jul 30 2016

A167810 Number of admissible basis in the postage stamp problem for n denominations and h = 3 stamps.

Original entry on oeis.org

1, 3, 13, 86, 760, 8518, 116278, 1911198, 37063964, 835779524, 21626042510, 635611172160, 21033034941826, 777710150809009

Offset: 1

Yogy Namara (yogy.namara(AT)gmail.com), Nov 12 2009

A basis 1 = b_1 < b_2 ... < b_n is admissible if all the values 1 <= x <= b_n is obtainable as a sum of at most h (not necessarily distinct) numbers in the basis.

R. K. Guy, Unsolved Problems in Number Theory, C12.

R. Alter and J. A. Barnett, A postage stamp problem, Amer. Math. Monthly, 87 (1980), 206-210.
M. F. Challis, Two new techniques for computing extremal h-bases A_k, Comp J 36(2) (1993) 117-126
Erich Friedman, Postage stamp problem
W. F. Lunnon, A postage stamp problem, Comput. J. 12 (1969) 377-380.
S. Mossige, Algorithms for Computing the h-Range of the Postage Stamp Problem, Math. Comp. 36 (1981) 575-582

Other enumerations with different parameters: A167809 (h = 2), A167810 (h = 3), A167811 (h = 4), A167812 (h = 5), A167813 (h = 6), A167814 (h = 7).
For h = 2, cf. A008932.
A152112 is essentially the same sequence by definition. [From Herbert Kociemba, Jul 14 2010]

Terms a(1) to a(12) verified and new terms a(13) and a(14) added by Herbert Kociemba, Jul 14 2010

A167811 Number of admissible basis in the postage stamp problem for n denominations and h = 4 stamps.

Original entry on oeis.org

1, 4, 26, 291, 4752, 109640, 3380466, 136053274, 6963328612, 444765731559

Offset: 1

Yogy Namara (yogy.namara(AT)gmail.com), Nov 12 2009

A basis 1 = b_1 < b_2 ... < b_n is admissible if all the values 1 <= x <= b_n is obtainable as a sum of at most h (not necessarily distinct) numbers in the basis.

R. K. Guy, Unsolved Problems in Number Theory, C12.

R. Alter and J. A. Barnett, A postage stamp problem, Amer. Math. Monthly, 87 (1980), 206-210.
M. F. Challis, Two new techniques for computing extremal h-bases A_k, Comp J 36(2) (1993) 117-126
Erich Friedman, Postage stamp problem
W. F. Lunnon, A postage stamp problem, Comput. J. 12 (1969) 377-380.
S. Mossige, Algorithms for Computing the h-Range of the Postage Stamp Problem, Math. Comp. 36 (1981) 575-582

Other enumerations with different parameters: A167809 (h = 2), A167810 (h = 3), A167811 (h = 4), A167812 (h = 5), A167813 (h = 6), A167814 (h = 7).

For h = 2, cf. A008932.

A167812 Number of admissible basis in the postage stamp problem for n denominations and h = 5 stamps.

Original entry on oeis.org

1, 5, 45, 750, 20881, 880325, 54329413, 4727396109, 563302698378

Offset: 1

Yogy Namara (yogy.namara(AT)gmail.com), Nov 12 2009

A basis 1 = b_1 < b_2 ... < b_n is admissible if all the values 1 <= x <= b_n is obtainable as a sum of at most h (not necessarily distinct) numbers in the basis.

R. K. Guy, Unsolved Problems in Number Theory, C12.

R. Alter and J. A. Barnett, A postage stamp problem, Amer. Math. Monthly, 87 (1980), 206-210.
M. F. Challis, Two new techniques for computing extremal h-bases A_k, Comp J 36(2) (1993) 117-126
Erich Friedman, Postage stamp problem
W. F. Lunnon, A postage stamp problem, Comput. J. 12 (1969) 377-380.
S. Mossige, Algorithms for Computing the h-Range of the Postage Stamp Problem, Math. Comp. 36 (1981) 575-582

Other enumerations with different parameters: A167809 (h = 2), A167810 (h = 3), A167811 (h = 4), A167812 (h = 5), A167813 (h = 6), A167814 (h = 7).

For h = 2, cf. A008932.

A167813 Number of admissible basis in the postage stamp problem for n denominations and h = 6 stamps.

Original entry on oeis.org

1, 6, 71, 1694, 73126, 5235791, 593539539, 102141195784

Offset: 1

Yogy Namara (yogy.namara(AT)gmail.com), Nov 12 2009

A basis 1 = b_1 < b_2 ... < b_n is admissible if all the values 1 <= x <= b_n is obtainable as a sum of at most h (not necessarily distinct) numbers in the basis.

R. K. Guy, Unsolved Problems in Number Theory, C12.

R. Alter and J. A. Barnett, A postage stamp problem, Amer. Math. Monthly, 87 (1980), 206-210.
M. F. Challis, Two new techniques for computing extremal h-bases A_k, Comp J 36(2) (1993) 117-126
Erich Friedman, Postage stamp problem
W. F. Lunnon, A postage stamp problem, Comput. J. 12 (1969) 377-380.
S. Mossige, Algorithms for Computing the h-Range of the Postage Stamp Problem, Math. Comp. 36 (1981) 575-582

Other enumerations with different parameters: A167809 (h = 2), A167810 (h = 3), A167811 (h = 4), A167812 (h = 5), A167813 (h = 6), A167814 (h = 7).

For h = 2, cf. A008932.

cp's OEIS Frontend

A167809 Number of admissible bases in the postage stamp problem for n denominations and h = 2 stamps.

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A167810 Number of admissible basis in the postage stamp problem for n denominations and h = 3 stamps.

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A167811 Number of admissible basis in the postage stamp problem for n denominations and h = 4 stamps.

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A167812 Number of admissible basis in the postage stamp problem for n denominations and h = 5 stamps.

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A167813 Number of admissible basis in the postage stamp problem for n denominations and h = 6 stamps.

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